- 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.
- The probability that a student does not have long hair.
- The probability that a student is a man or has short hair.
- The probability that a student is a woman and has long hair.
- The probability that a student is a man, given that the student has long hair.
- The probability that a student has long hair, given that the student is a man.
- Of all the women students, the probability that a student has short hair.
- Of all students with long hair, the probability that a student is a woman.
- The probability that a student is a woman or has long hair.
- The probability that a randomly selected student is a man student with short hair.
- 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.
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.
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.
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.
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.
Let F = event that book is fiction
Let N = event that book is nonfiction
What is the sample space?
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.
3.2 Independent and Mutually Exclusive Events
a. \(P(U \cap V)=\)
b. \(P(U \mid V)=\)
c. \(P(U \cup V)=\)
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:
- \(Z=\) event that a customer orders a pizza
- \(S=\) event that a customer orders a salad
Suppose that one customer is randomly selected.
44. Find \(P(Z)\).
45. Find \(P(S)\).
46. Find \(P(S \mid Z)\).
47. In words, what is \(S \mid Z\) ?
48. Find \(P(Z \cap S)\).
49. In words, what is \(Z \cap S\) ?
50. Are \(P\) and \(S\) independent events? Show why or why not.
51. Find \(P(Z \cup S)\).
52. In words, what is \(Z \cup S\) ?
53. 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.
Gender | Self-taught | Studied in School | Private Instruction | Total |
---|---|---|---|---|
Woman | 12 | 38 | 22 | 72 |
Man | 19 | 24 | 15 | 58 |
Total | 31 | 62 | 37 | 130 |
57. Are the events "being a woman musician" and "learning music in school" mutually exclusive events?