Deck 11: Probability Basics

Question 1

Use the following
For two events A and B, we have P(A) =0.47, P(B) = 0.33, and P(A and B) = 0.20.
-Find P(not A). Use two decimal places.

Answer 1

0.53

Question 2

Use the following
For two events A and B, we have P(A) =0.47, P(B) = 0.33, and P(A and B) = 0.20.
-Find P(not B). Use two decimal places.

Answer 2

0.67

Question 3

Use the following
For two events A and B, we have P(A) =0.47, P(B) = 0.33, and P(A and B) = 0.20.
-Find P(A or B). Use two decimal places.

Answer 3

0.6

Question 4

Use the following
For two events A and B, we have P(A) =0.47, P(B) = 0.33, and P(A and B) = 0.20.
-Find P(A if B). Use three decimal places.

Question 5

Use the following
For two events A and B, we have P(A) =0.47, P(B) = 0.33, and P(A and B) = 0.20.
-Find P(B if A). Use three decimal places.

Question 6

Use the following
For two events A and B, we have P(A) =0.47, P(B) = 0.33, and P(A and B) = 0.20.
-Are events A and B disjoint? Explain briefly.

Question 7

Use the following
Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified.
-Find P(not A).

Question 8

Use the following
Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified.
-Find P(not B).

Question 9

Use the following
Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified.
-Find P(A or B). Use four decimal places.

Question 10

Use the following
Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified.
-Find P(A if B).

Question 11

Use the following
Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified.
-Find P(B if A).

Question 12

Use the following
Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified.
-Are events A and B disjoint? Explain briefly.

Question 13

Use the following
Suppose A and B are independent events with P(A) = 0.21 and P(B) = 0.81.
-Find P(A if B). Use two decimal places.

Question 14

Use the following
Suppose A and B are independent events with P(A) = 0.21 and P(B) = 0.81.
-Find P(B if A). Use two decimal places.

Question 15

Use the following
Suppose A and B are independent events with P(A) = 0.21 and P(B) = 0.81.
-Find P(A and B). Round your answer to four decimal places.

Question 16

Use the following
Suppose A and B are independent events with P(A) = 0.21 and P(B) = 0.81.
-Find P(A or B). Round your answer to four decimal places.

Question 17

Use the following
Consider rolling a fair six-sided die. Round all answers to three decimal places.
-What is the probability that the result of rolling the die is a 3?

Question 18

Use the following
Consider rolling a fair six-sided die. Round all answers to three decimal places.
-What is the probability that the result is not a 5?

Question 19

Use the following
Consider rolling a fair six-sided die. Round all answers to three decimal places.
-What is the probability that the result is a 2 or a 4?

Question 20

Use the following
Consider rolling a fair six-sided die. Round all answers to three decimal places.
-Suppose we record the result of the roll and then roll the die a second time. What is the probability that both rolls are a 6?

Question 21

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-What is the probability that a randomly selected student in the class has green eyes?

Question 22

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-What is the probability that a randomly selected student is a female?

Question 23

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-What is the probability that a randomly selected student in the class is a female and has hazel eyes?

Question 24

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-What is the probability that a randomly selected student does not have green eyes?

Question 25

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-What is the probability that a randomly selected student in the class is a female or has brown eyes?

Question 26

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-What is the probability that a randomly selected student has blue eyes if we know they are female?

Question 27

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-What is the probability that a randomly selected student is a male, if we know that they have hazel eyes?

Question 28

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-Are male and blue eyes independent? Briefly justify your answer.

Question 29

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-Are brown and blue eyes disjoint? Explain briefly.

Question 30

Use the following
On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table.
Round your answer to each question to three decimal places.
-Are hazel eyes and male disjoint? Explain briefly.

Question 31

Use the following
A bag of peanut butter M&M's contains 188 candies. Of the candies, 28 are blue, 40 are brown, 38 are green, 25 are orange, 34 are red, and 23 are yellow. They are thoroughly mixed up so that each is equally likely to be selected if we pick one. Round all of your answers to four decimal places.
-If we select one M&M at random, what is the probability that it is brown?

Question 32

Use the following
A bag of peanut butter M&M's contains 188 candies. Of the candies, 28 are blue, 40 are brown, 38 are green, 25 are orange, 34 are red, and 23 are yellow. They are thoroughly mixed up so that each is equally likely to be selected if we pick one. Round all of your answers to four decimal places.
-If we select one M&M at random, what is the probability that it is not red?

Question 33

Use the following
A bag of peanut butter M&M's contains 188 candies. Of the candies, 28 are blue, 40 are brown, 38 are green, 25 are orange, 34 are red, and 23 are yellow. They are thoroughly mixed up so that each is equally likely to be selected if we pick one. Round all of your answers to four decimal places.
-If we select one M&M at random, what is the probability that it is orange or yellow?

Question 34

Use the following
A bag of peanut butter M&M's contains 188 candies. Of the candies, 28 are blue, 40 are brown, 38 are green, 25 are orange, 34 are red, and 23 are yellow. They are thoroughly mixed up so that each is equally likely to be selected if we pick one. Round all of your answers to four decimal places.
-If we select one at random, then put it back, mix them up well (so the selections are independent) and select another one, what is the probability that both the first and second M&M's are blue?

Question 35

Use the following
A bag of peanut butter M&M's contains 188 candies. Of the candies, 28 are blue, 40 are brown, 38 are green, 25 are orange, 34 are red, and 23 are yellow. They are thoroughly mixed up so that each is equally likely to be selected if we pick one. Round all of your answers to four decimal places.
-If we select one, keep it, and then select a second one, what is the probability that the first one is yellow and the second one is blue?

Question 36

Use the following
Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places.

-P(B and X)

Question 37

Use the following
Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places.

-P(A and Y)

Question 38

Use the following
Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places.

-P(Y if A)

Question 39

Use the following
Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places.

-P(X if B)

Question 40

Use the following
Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places.

-P(Y)

Question 41

Use the following
Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places.

-P(X)

Question 42

Use the following
Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places.

-P(A if X)

Question 43

Use the following
Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places.

-P(B if Y)

Question 44

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-a

Question 45

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-b

Question 46

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-c

Question 47

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-d

Question 48

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-P(X)

Question 49

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-P(Y)

Question 50

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-P(I if X)

Question 51

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-P(II if X)

Question 52

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-P(I if Y)

Question 53

Use the following
A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places.

-P(III if Y)

Question 54

Use the following
There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied.
Round all answers to four decimal places.
-What is the probability that a randomly selected customer used Al's Roof Repair and is dissatisfied?

Question 55

Use the following
There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied.
Round all answers to four decimal places.
-What is the probability that a randomly selected customer used Bob's Better Building and is satisfied?

Question 56

Use the following
There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied.
Round all answers to four decimal places.
-What proportion of roofing customers are satisfied?

Question 57

Use the following
There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied.
Round all answers to four decimal places.
-What proportion of roofing customers are satisfied?

Question 58

Use the following
There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied.
Round all answers to four decimal places.
-If a randomly selected customer is satisfied, what is the probability that they used Al's Roof Repair?

Question 59

Use the following
There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied.
Round all answers to four decimal places.
-If a randomly selected customer is dissatisfied, what is the probability they used Bob's Better Building?

Question 60

Use the following
There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied.
Round all answers to four decimal places.
-If a randomly selected customer is dissatisfied, what is the probability that they used Al's Roof Repair?

Question 61

Use the following
There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied.
Round all answers to four decimal places.
-If a randomly selected customer is satisfied, what is the probability that they used Carl's Roof Service?

Question 62

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-What is the probability that the knife is the murder weapon?

Question 63

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-What is the probability that the lead pipe is the murder weapon?

Question 64

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-What is the probability that the rope is the murder weapon?

Question 65

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-Suppose while playing the game you discover that the lead pipe is the murder weapon. Given this information, what is the probability that Colonel Mustard is the murderer?

Question 66

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-Suppose while playing the game you discover that the rope is the murder weapon. Given this information, what is the probability that the murderer is Miss Scarlet?

Question 67

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-Suppose while playing the game you discover that the rope is the murder weapon. Given this information, what is the probability that Colonel Mustard is the murderer?

Question 68

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-Suppose while playing the game you discover that the knife is the murder weapon. Given this information, what is the probability that Professor Plum is the murderer?

Question 69

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-Suppose while playing the game you discover that the knife is the murder weapon. Given this information, what is the probability that Miss Scarlet is the murderer?

Question 70

Use the following
A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope.
Round all answers to three decimal places.
-Suppose while playing the game you discover that the lead pipe is the murder weapon. Given this information, what is the probability that Professor Plum is the murderer?

Question 71

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Find P(X = 3).

Question 72

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Find P(X = 1 or X = 2).

Question 73

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Find P(X > 2).

Question 74

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Find P(X < 2).

Question 75

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Find P(X 2).

Question 76

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Find P(X is odd).

Question 77

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Find P(X is even).

Question 78

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Compute the mean of the random variable X.

Question 79

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Compute the variance of the random variable X.

Question 80

Use the following
A random variable X has the following probability function:

Round all answers to two decimal places.
-Compute the standard deviation of the random variable X.