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

In a particular college class, there are men and women 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. (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 W be the event that a student is a woman.

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

• 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 a man or has short hair.

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

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

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

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

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

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

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

j. The probability that a student is a woman.

Use the following information to answer the next four exercises. A box is filled with several party favors. It contains 12 hats, 15 noisemakers, ten finger traps, and five bags of confetti. One party favor is chosen from the box at random.
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, ten finger traps, and five bags of confetti. One party favor is chosen from the box at random.
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. One jelly bean is chosen from the box at random.
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. One jelly bean is chosen from the box at random.
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. One jelly bean is chosen from the box at random.
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 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 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 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 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 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 ten 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 ten 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 ten 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 ten 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 ten 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 ten 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 ten 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 ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

Find P(Z).

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

Find P(S).

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

Find P(S|Z).

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

In words, what is S|Z?

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

Find $P(Z AND S)$.

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

In words, what is $Z AND S$?

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

Are P and S independent events? Show why or why not.

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

Find $P(Z OR S)$.

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

In words, what is $Z OR S$?

Use the following information to answer the next ten exercises. A local restaurant knows that the probability that a customer will order a pizza is 87%. The restaurant also knows that the probability that a customer will order a salad is 32%. Of the customers who order pizzas, 55% of them also order a salad.

In this problem, let:

Suppose that one customer is randomly selected.

Are Z and S 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 man 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 woman 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 smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispanic/Latino people, 8,378 Japanese people, and 7,650 White people. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 Black people, 3,062 Native Hawaiian people, 4,932 Hispanic/Latino people, 10,680 Japanese people, and 9,877 White people. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 Black people, 1,419 Native Hawaiian people, 1,406 Hispanic/Latino people, 4,715 Japanese people, and 6,062 White people. Of the people smoking at least 31 cigarettes per day, there were 759 Black people, 788 Native Hawaiian people, 800 Hispanic/Latino people, 2,305 Japanese people, and 3,970 White people.

Suppose that one person from the study is randomly selected. Find the probability that person smoked 11 to 20 cigarettes 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 smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispanic/Latino people, 8,378 Japanese people, and 7,650 White people. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 Black people, 3,062 Native Hawaiian people, 4,932 Hispanic/Latino people, 10,680 Japanese people, and 9,877 White people. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 Black people, 1,419 Native Hawaiian people, 1,406 Hispanic/Latino people, 4,715 Japanese people, and 6,062 White people. Of the people smoking at least 31 cigarettes per day, there were 759 Black people, 788 Native Hawaiian people, 800 Hispanic/Latino people, 2,305 Japanese people, and 3,970 White people.

In words, explain what it means to pick one person from the study who is “Japanese American AND smokes 21 to 30 cigarettes 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 smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispanic/Latino people, 8,378 Japanese people, and 7,650 White people. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 Black people, 3,062 Native Hawaiian people, 4,932 Hispanic/Latino people, 10,680 Japanese people, and 9,877 White people. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 Black people, 1,419 Native Hawaiian people, 1,406 Hispanic/Latino people, 4,715 Japanese people, and 6,062 White people. Of the people smoking at least 31 cigarettes per day, there were 759 Black people, 788 Native Hawaiian people, 800 Hispanic/Latino people, 2,305 Japanese people, and 3,970 White people.

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

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

a. If there is a 60% chance of rain on Saturday and a 70% chance of rain on Sunday, then there is a 130% 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.

A survey was conducted in a large city to measure the popularity of that city’s mayor. The survey was repeated every year for three years. The survey polled 1,046 people to measure the mayor’s popularity. Everyone polled expressed either approval or disapproval. These are the results the poll produced:

• In Year 1, 60% of the population approved of the mayor’s actions in office.

• In Year 2, 57% of the population approved of his actions.

• In Year 3, the percentage of popular approval was measured at 42%.

a. What is the sample size for this study?

b. What proportion in the poll disapproved of the mayor, according to the results from Year 3?

c. How many people polled responded that they approved the mayor based on results from Year 3?

d. What is the probability that a person supported the mayor, based on the data collected in Year 2?

e. What is the probability that a person supported the mayor, based on the data collected in Year 1?

Use the following information to answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.

Compute the probability of winning the following types of bets:

a. Betting on two lines that touch each other on the table as in 1-2-3-4-5-6

b. Betting on three numbers in a line, as in 1-2-3

c. Betting on one number

d. Betting on four numbers that touch each other to form a square, as in 10-11-13-14

e. Betting on two numbers that touch each other on the table, as in 10-11 or 10-13

f. Betting on 0-00-1-2-3

g. Betting on 0-1-2; or 0-00-2; or 00-2-3

Use the following information to answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.

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. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.

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. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.

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) = 0.71 and P(Y) = 0.42.

Use the following information to answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.

According to the 2019 U.S. Census, approximately 331,449,281 people live in the United States. Of these people, 67,800,000 speak a language other than English at home. Of those who speak another language at home, 61.6% speak Spanish.

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

Finish each probability statement by matching the correct answer.

Use the following information to answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.

According to the American Red Cross, a person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any blood type. Their data show that 45% of people have type O blood and 7% of people have Rh- factor; 38% 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. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.

In a box of assorted cookies, 36% contain chocolate and 12% contain nuts. In the box, 8% 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 3.20 to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

What is the probability that a randomly selected senator has an “Other” affiliation?

Use the information in the Table 3.20 to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

What is the probability that a randomly selected senator is a Democrat and up for reelection in Year B?

Use the information in the Table 3.20 to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

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

Use the information in the Table 3.20 to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

The events “Republican” and “Up for reelection in Year B” 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. $\frac{4189}{12351}$

b. $\frac{117}{1723}$

c. $\frac{1723}{4189}$

d. $\frac{117}{12351}$

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 person develops cancer is 0.4567. The probability that a person has at least one false positive test result (meaning the test comes back for cancer when the person does not have it) is 0.51. 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 person develops cancer and P = a person 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 a male has cancer? Justify numerically and explain why or why not.

Given events J and K: P(J) = 0.18; P(K) = 0.37; P(J OR K) = 0.45

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) that are women is 48.60. Of the women, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Of the licensed U.S. men drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.

Complete the following.

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

b. Find P(driver is a woman).

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

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

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 a woman 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) that are women is 48.60. Of the women, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Of the licensed U.S. men drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.

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

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

Answer these questions using probability rules. Do NOT use the contingency table. A total of 6,481 new vehicles were purchased over a monthly time period in a certain county. These purchases will be our population. Of these purchases, 36% were made by people in their twenties, and 42% were purchases of sedans. 20% of purchases were for sedans purchased by people in their twenties.

a. Find P(Person is in their twenties).

b. Find P(Person purchased a sedan).

c. Find P(Person is in their twenties GIVEN person purchased a sedan)