Chapter 3: Probability TopicsContent check — Statistics, Chapter 3: Probability Topics

In a particular college class, there are male and female students. Some students have long hair and some students have short hair. Write the symbols for the probabilities of the events for parts A through J of this question. Note that you cannot find numerical answers here. You were not given enough information to find any probability values yet; concentrate on understanding the symbols.

• Let F be the event that a student is female.

• Let M be the event that a student is male.

• Let S be the event that a student has short hair.

• Let L be the event that a student has long hair.

a. The probability that a student does not have long hair.

b. The probability that a student is male or has short hair.

c. The probability that a student is female and has long hair.

d. The probability that a student is male, given that the student has long hair.

e. The probability that a student has long hair, given that the student is male.

f. Of all female students, the probability that a student has short hair.

g. Of all students with long hair, the probability that a student is female.

h. The probability that a student is female or has long hair.

i. The probability that a randomly selected student is a male student with short hair.

j. The probability that a student is female.

Use the following information to answer the next four exercises. A box is filled with several party favors. It contains 12 hats, 15 noisemakers, 10 finger traps, and five bags of confetti.
Let H = the event of getting a hat.
Let N = the event of getting a noisemaker.
Let F = the event of getting a finger trap.
Let C = the event of getting a bag of confetti.

Find P(N).

Use the following information to answer the next four exercises. A box is filled with several party favors. It contains 12 hats, 15 noisemakers, 10 finger traps, and five bags of confetti.
Let H = the event of getting a hat.
Let N = the event of getting a noisemaker.
Let F = the event of getting a finger trap.
Let C = the event of getting a bag of confetti.

Find P(C).

Use the following information to answer the next six exercises. A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange.
Let B = the event of getting a blue jelly bean
Let G = the event of getting a green jelly bean.
Let O = the event of getting an orange jelly bean.
Let P = the event of getting a purple jelly bean.
Let R = the event of getting a red jelly bean.
Let Y = the event of getting a yellow jelly bean.

Find P(G).

Use the following information to answer the next six exercises. A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange.
Let B = the event of getting a blue jelly bean
Let G = the event of getting a green jelly bean.
Let O = the event of getting an orange jelly bean.
Let P = the event of getting a purple jelly bean.
Let R = the event of getting a red jelly bean.
Let Y = the event of getting a yellow jelly bean.

Find P(R).

Use the following information to answer the next six exercises. A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange.
Let B = the event of getting a blue jelly bean
Let G = the event of getting a green jelly bean.
Let O = the event of getting an orange jelly bean.
Let P = the event of getting a purple jelly bean.
Let R = the event of getting a red jelly bean.
Let Y = the event of getting a yellow jelly bean.

Find P(O).

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 countries in Oceania (Pacific Ocean region).
Let A = the event that a country is in Asia.
Let E = the event that a country is in Europe.
Let F = the event that a country is in Africa.
Let N = the event that a country is in North America.
Let O = the event that a country is in Oceania.
Let S = the event that a country is in South America.

Find P(E).

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 countries in Oceania (Pacific Ocean region).
Let A = the event that a country is in Asia.
Let E = the event that a country is in Europe.
Let F = the event that a country is in Africa.
Let N = the event that a country is in North America.
Let O = the event that a country is in Oceania.
Let S = the event that a country is in South America.

Find P(N).

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 countries in Oceania (Pacific Ocean region).
Let A = the event that a country is in Asia.
Let E = the event that a country is in Europe.
Let F = the event that a country is in Africa.
Let N = the event that a country is in North America.
Let O = the event that a country is in Oceania.
Let S = the event that a country is in South America.

Find P(S).

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 countries in Oceania (Pacific Ocean region).
Let A = the event that a country is in Asia.
Let E = the event that a country is in Europe.
Let F = the event that a country is in Africa.
Let N = the event that a country is in North America.
Let O = the event that a country is in Oceania.
Let S = the event that a country is in South America.

What is the probability of drawing a club in a standard deck of 52 cards?

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 countries in Oceania (Pacific Ocean region).
Let A = the event that a country is in Asia.
Let E = the event that a country is in Europe.
Let F = the event that a country is in Africa.
Let N = the event that a country is in North America.
Let O = the event that a country is in Oceania.
Let S = the event that a country is in South America.

What is the probability of rolling a prime number of dots with a fair, six-sided die numbered one through six?

Use the following information to answer the next two exercises. You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area.

Let B = the event of landing on blue.
Let R = the event of landing on red.
Let G = the event of landing on green.
Let Y = the event of landing on yellow.

If you land on red, you don’t get a prize. What is P(R)?

Use the following information to answer the next 10 exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.
Let I = the event that a player in an infielder.
Let O = the event that a player is an outfielder.
Let H = the event that a player is a great hitter.
Let N = the event that a player is not a great hitter.

Write the symbols for the probability that a player is an outfielder or is a great hitter.

Use the following information to answer the next 10 exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.
Let I = the event that a player in an infielder.
Let O = the event that a player is an outfielder.
Let H = the event that a player is a great hitter.
Let N = the event that a player is not a great hitter.

Write the symbols for the probability that a player is a great hitter, given that the player is an infielder.

Use the following information to answer the next 10 exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.
Let I = the event that a player in an infielder.
Let O = the event that a player is an outfielder.
Let H = the event that a player is a great hitter.
Let N = the event that a player is not a great hitter.

Write the symbols for the probability that of all the outfielders, a player is not a great hitter.

Use the following information to answer the next 10 exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.
Let I = the event that a player in an infielder.
Let O = the event that a player is an outfielder.
Let H = the event that a player is a great hitter.
Let N = the event that a player is not a great hitter.

Write the symbols for the probability that a player is an infielder or is not a great hitter.

Use the following information to answer the next 10 exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.
Let I = the event that a player in an infielder.
Let O = the event that a player is an outfielder.
Let H = the event that a player is a great hitter.
Let N = the event that a player is not a great hitter.

Write the symbols for the probability that a player is an infielder.

Use the following information to answer the next 10 exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.
Let I = the event that a player in an infielder.
Let O = the event that a player is an outfielder.
Let H = the event that a player is a great hitter.
Let N = the event that a player is not a great hitter.

What is conditional probability?

Use the following information to answer the next 10 exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.
Let I = the event that a player in an infielder.
Let O = the event that a player is an outfielder.
Let H = the event that a player is a great hitter.
Let N = the event that a player is not a great hitter.

What is the sum of the probabilities of an event and its complement?

Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three.

What does P(E OR M) mean in words?

Use the following information to answer the next 10 exercises. Forty-eight percent of all voters of a certain state prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Among Latino registered voters in this state, 55 percent prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Of all citizens in this state, 37.6 percent are Latino.

In this problem, let

Suppose that one citizen is randomly selected.

Find P(L).

Use the following information to answer the next 10 exercises. Forty-eight percent of all voters of a certain state prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Among Latino registered voters in this state, 55 percent prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Of all citizens in this state, 37.6 percent are Latino.

In this problem, let

Suppose that one citizen is randomly selected.

In words, what is C|L?

Use the following information to answer the next 10 exercises. Forty-eight percent of all voters of a certain state prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Among Latino registered voters in this state, 55 percent prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Of all citizens in this state, 37.6 percent are Latino.

In this problem, let

Suppose that one citizen is randomly selected.

In words, what is L AND C?

Use the following information to answer the next 10 exercises. Forty-eight percent of all voters of a certain state prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Among Latino registered voters in this state, 55 percent prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Of all citizens in this state, 37.6 percent are Latino.

In this problem, let

Suppose that one citizen is randomly selected.

Find P(L OR C).

Use the following information to answer the next 10 exercises. Forty-eight percent of all voters of a certain state prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Among Latino registered voters in this state, 55 percent prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Of all citizens in this state, 37.6 percent are Latino.

In this problem, let

Suppose that one citizen is randomly selected.

Are L and C mutually exclusive events? Show why or why not.

Use the following information to answer the next four exercises. Table 3.16 shows a random sample of musicians and how they learned to play their instruments.

Find P(musician is a male AND had private instruction).

Use the following information to answer the next four exercises. Table 3.16 shows a random sample of musicians and how they learned to play their instruments.

Are the events being a female musician and learning music in school mutually exclusive events?

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of people who use a product in California and Hawaii. In one part of the report, the self-reported ethnicity and using the product levels per day were given. Of the people using the product at most 10 times a day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 whites. Of the people using the product 11 to 20 times per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people using the product 21 to 30 times per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 Whites. Of the people using the product at least 31 times per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites.

Suppose that one person from the study is randomly selected. Find the probability that the person used the product 11 to 20 times per day.

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of people who use a product in California and Hawaii. In one part of the report, the self-reported ethnicity and using the product levels per day were given. Of the people using the product at most 10 times a day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 whites. Of the people using the product 11 to 20 times per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people using the product 21 to 30 times per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 Whites. Of the people using the product at least 31 times per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites.

In words, explain what it means to pick one person from the study who is Japanese American AND uses the product 21 to 30 times per day. Also, find the probability.

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of people who use a product in California and Hawaii. In one part of the report, the self-reported ethnicity and using the product levels per day were given. Of the people using the product at most 10 times a day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 whites. Of the people using the product 11 to 20 times per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people using the product 21 to 30 times per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 Whites. Of the people using the product at least 31 times per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites.

In words, explain what it means to pick one person from the study who is Japanese American GIVEN that the person uses the product 21 to 30 times per day. Also, find the probability.

Explain what is wrong with the following statements. Use complete sentences.

a. If there is a 60 percent chance of rain on Saturday and a 70 percent chance of rain on Sunday, then there is a 130 percent chance of rain over the weekend.

b. The probability that a baseball player hits a home run is greater than the probability that he gets a successful hit.

Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Health Index Scores are the sample space. We randomly sample one type of Health Index Score, the emotional well-being score.

Find the probability that a Health Index Score is 81.0.

Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Health Index Scores are the sample space. We randomly sample one type of Health Index Score, the emotional well-being score.

Find the probability that a Health Index Score is between 80.5 and 82.

Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Health Index Scores are the sample space. We randomly sample one type of Health Index Score, the emotional well-being score.

What is the probability that a Health Index Score is 80.7 or 82.7?

Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Health Index Scores are the sample space. We randomly sample one type of Health Index Score, the emotional well-being score.

What occupation has the highest Health Index Score?

Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Health Index Scores are the sample space. We randomly sample one type of Health Index Score, the emotional well-being score.

What is the range of the data?

Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Health Index Scores are the sample space. We randomly sample one type of Health Index Score, the emotional well-being score.

If all occupations are equally likely for a certain individual, what is the probability that he or she will have an occupation with lower than average Health Index Score?

After a mayor of a major Canadian city announced his plans to cut budget costs in late 2011, researchers polled 1,046 people to measure the mayor’s popularity. Everyone polled expressed either approval or disapproval. These are the results their poll produced:

• In early 2011, 60 percent of the population approved of the mayor's actions in office.

• In mid-2011, 57 percent of the population approved of his actions.

• In late 2011, the percentage of popular approval was measured at 42 percent.

a. What is the sample size for this study?

b. What proportion in the poll disapproved of the mayor, according to the results from late 2011?

c. How many people polled responded that they approved of the mayor in late 2011?

d. What is the probability that a person supported the mayor, based on the data collected in mid-2011?

e. What is the probability that a person supported the mayor, based on the data collected in early 2011?

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

a. List the sample space of the possible items that are on the menu.

b. Find P(you will get a 17-oz. piece of meat).

c. Find P(you will get a pork chop).

d. Find P(you will get a 17-oz. pork chop).

e. Is getting a pork chop the complement of getting a chicken breast? Why?

f. Find two mutually exclusive events.

g. Are the events getting 17 oz. of meat and getting a pork chop independent?

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

Compute the probabilities.

a. P(you will get a chicken breast)

b. P(you will get a 17-oz. chicken breast)

c. P(you will get a chicken breast or you will not get a 17-oz. pork chop)

d. P(you will not get a chicken breast and you will get an 18-oz. pork chop)

e. P(you will get a piece of meat that is not 21 oz.)

f. P(you will get a piece of chicken that is not 21 oz.)

g. P(you will not get a chicken breast and you will not get a pork chop)

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

Compute the probabilities:

a. P(you will not get a pork chop)

b. P(you will get a 20-oz. pork chop)

c. P(you will not get a chicken breast or you will not get an 18-oz. pork chop)

d. P(you will not get a chicken breast and you will not get an 18-oz. pork chop)

e. P(you will get a pork chop that is not 21 oz.)

f. P(you will not get a chicken breast or you will not get a pork chop)

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.

• G = card drawn is green

• E = card drawn is even-numbered

a. List the sample space.

b. P(G) = ________

c. P(G|E) = ________

d. P(G AND E) = ________

e. P(G OR E) = ________

f. Are G and E mutually exclusive? Justify your answer numerically.

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

An experiment consists of tossing a nickel, a dime, and a quarter. Of interest is the side the coin lands on.

a. List the sample space.

b. Let A be the event that there are at least two tails. Find P(A).

c. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including justification.

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

Y and Z are independent events.

a. Rewrite the basic Addition Rule P(Y OR Z) = P(Y) + P(Z) - P(Y AND Z) using the information that Y and Z are independent events.

b. Use the rewritten rule to find P(Z) if P(Y OR Z) = .71 and P(Y) = .42.

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

Approximately 281,000,000 people over age five live in the United States. Of these people, 55,000,000 speak a language other than English at home. Of those who speak another language at home, 62.3 percent speak Spanish.

Let E = speaks English at home; E′ = speaks another language at home; and S = speaks Spanish.

Finish each probability statement by matching the correct answer.

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

United Blood Services is a blood bank that serves more than 500 hospitals in 18 states. According to their website, a person with type O blood and a negative Rh factor (Rh–) can donate blood to any person with any bloodtype. Their data show that 43 percent of people have type O blood and 15 percent of people have Rh– factor; 52 percent of people have type O or Rh– factor.

a. Find the probability that a person has both type O blood and the Rh– factor.

b. Find the probability that a person does not have both type O blood and the Rh– factor.

Use the following information to answer the next three exercises. A local restaurant sells pork chops and chicken breasts. The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu. Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.

In a box of assorted cookies, 36 percent contain chocolate and 12 percent contain nuts. Of those, 8 percent contain both chocolate and nuts. Sean is allergic to both chocolate and nuts.

a. Find the probability that a cookie contains chocolate or nuts (he can't eat it).

b. Find the probability that a cookie does not contain chocolate or nuts (he can eat it).

Use the information in the Table 3.21 to answer the next eight exercises. The table shows the political party affiliation of each of 67 members of the U.S. Senate in June 2012, and when they would next be up for reelection.

What is the probability that a randomly selected senator had an Other affiliation?

Use the information in the Table 3.21 to answer the next eight exercises. The table shows the political party affiliation of each of 67 members of the U.S. Senate in June 2012, and when they would next be up for reelection.

What is the probability that a randomly selected senator was a Democrat and was up for reelection in November 2016?

Use the information in the Table 3.21 to answer the next eight exercises. The table shows the political party affiliation of each of 67 members of the U.S. Senate in June 2012, and when they would next be up for reelection.

Suppose that a member of the U.S. Senate is randomly selected. Given that the randomly selected senator was up for reelection in November 2016, what is the probability that this senator was a Democrat?

Use the information in the Table 3.21 to answer the next eight exercises. The table shows the political party affiliation of each of 67 members of the U.S. Senate in June 2012, and when they would next be up for reelection.

The events Republican and Up for reelection in 2016 are ________.

a. mutually exclusive

b. independent

c. both mutually exclusive and independent

d. neither mutually exclusive nor independent

Use the following information to answer the next two exercises. The table of data obtained from www.baseball-almanac.com shows hit information for four well-known baseball players. Suppose that one hit from the table is randomly selected.

Find P(Hit was made by Ty Cobb|The hit was a Home Run).

a. $\frac{\mathrm{4,189}}{\mathrm{12,351}}$

b. $\frac{114}{\mathrm{1,720}}$

c. $\frac{\mathrm{1,720}}{\mathrm{4,189}}$

d. $\frac{114}{\mathrm{12,351}}$

Use the following information to answer the next two exercises. This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y), and five blue (B) beads. For the coin, P(H) = $\frac{2}{3}$ and P(T) = $\frac{1}{3}$ where H is heads and T is tails.

Find P(blue bead).

a. $\frac{15}{36}$

b. $\frac{10}{36}$

c. $\frac{10}{12}$

d. $\frac{6}{36}$

The probability that a male develops some form of cancer in his lifetime is .4567. The probability that a male has at least one false-positive test result, meaning the test comes back for cancer when the man does not have it, is .51. Some of the following questions do not have enough information for you to answer them. Write not enough information for those answers. Let C = a man develops cancer in his lifetime and P = a man has at least one false-positive.

a. P(C) = ______

b. P(P|C) = ______

c. P(P|C') = ______

d. If a test comes up positive, based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not.

Given events J and K: P(J) = .18; P(K) = .37; P(J OR K) = .45

a. Find P(J AND K).

b. Find the probability of the complement of event (J AND K).

c. Find the probability of the complement of event (J OR K).

Use the following information to answer the next two exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled.

Suppose that you randomly draw two cards, one at a time, with replacement.
Let G₁ = first card is green
Let G₂ = second card is green

a. Draw a tree diagram of the situation.

b. Find P(G₁ AND G₂).

c. Find P(at least one green).

d. Find P(G₂|G₁).

e. Are G₂ and G₁ independent events? Explain why or why not.

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) who are female is 48.60. Of the females, 5.03 percent are age 19 and under; 81.36 percent are age 20–64; 13.61 percent are age 65 or over. Of the licensed U.S. male drivers, 5.04 percent are age 19 and under; 81.43 percent are age 20–64; 13.53 percent are age 65 or over.

Complete the following:

a. Construct a table or a tree diagram of the situation.

b. Find P(driver is female).

c. Find P(driver is age 65 or over|driver is female).

d. Find P(driver is age 65 or over AND female).

e. In words, explain the difference between the probabilities in Part c and Part d.

f. Find P(driver is age 65 or over).

g. Are being age 65 or over and being female mutually exclusive events? How do you know?

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) who are female is 48.60. Of the females, 5.03 percent are age 19 and under; 81.36 percent are age 20–64; 13.61 percent are age 65 or over. Of the licensed U.S. male drivers, 5.04 percent are age 19 and under; 81.43 percent are age 20–64; 13.53 percent are age 65 or over.

Approximately 86.5 percent of Americans commute to work by car, truck, or van. Out of that group, 84.6 percent drive alone and 15.4 percent drive in a carpool. Approximately 3.9 percent walk to work and approximately 5.3 percent take public transportation.

a. Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.

b. Assuming that the walkers walk alone, what percent of all commuters travel alone to work?

c. Suppose that 1,000 workers are randomly selected. How many would you expect to travel alone to work?

d. Suppose that 1,000 workers are randomly selected. How many would you expect to drive in a carpool?