**Question**

The event of eating breakfast at a diner is A and the event of watching cable is B. If these events are independent events, using P(A)=0.22, and P(B)=0.46, what is P(B|A)?

# Question

The event the number 9 car wins the race is A and the event the number 8 car wins the race is B. If these events are mutually exclusive events, using P(A)=0.39, and P(B)=0.31, what is P(A|B)?

**Question**

The following information about undergraduates at a university is given:

- The probability that a randomly chosen undergraduate attends office hours is 24%;
- The probability that a randomly chosen undergraduate has a 30GPA or higher is 15.5%;
- The probability that a random chosen undergraduate has a 30GPA or higher given that they attend office hours is 12%.

Let event A is an undergraduate attending office hours and event B is an undergraduate having a 3.30 or higher GPA. Are events A and B mutually exclusive, independent, both, or neither?

# Question

Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis.

Given the three events, which of the following statements is true? Select all that apply.

Event A: The mother or father carries the recessive gene.

Event B: The father carries the recessive gene.

Event C: The baby is at risk for Cystic Fibrosis.

# Question

You have a standard deck of 52 cards. There are four suits: clubs, diamonds, hearts, and spades. Each suit has 13 cards: Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King. Given Events A and B, are the two events mutually exclusive? Explain your answer.

Event A: Drawing a 10.

Event B: Drawing a heart.

### Correct answer:

No, the events are not mutually exclusive because they share the common outcome of 10 of hearts.

Given the following information about events B and C:

- P(B)=70%
- P(B AND C)=0
- P(C)=45%

Are B and C mutually exclusive, independent, both, or neither?

### Correct answer:

B and C are mutually exclusive because P(B AND C)=0.

**Question**

Consider the Venn diagram below. Each of the dots outside the circle represents a city that’s population growth was studied. In this experiment, 7 cities are studied. The cities were: Austin, Charlotte, Chicago, Duluth, Minneapolis, New York, and Seattle.

The two events represented in the Venn diagram are:

- Event A: The city has positive population growth over the past five years.
- Event B: The city has positive economic growth over the past five years.

Austin, Charlotte, Chicago, New York, and Seattle reported that they have had positive population growth over the past five years. Minneapolis, New York, and Seattle reported that they have had positive economic growth over the past five years. Duluth stated that neither option applied to them.

Place the dots in the appropriate event given the information above (you may not use all of the dots), then determine if the events are **mutually exclusive.**

# Question

The event of using your free hour to nap is A and the event of using your free hour to study is B. If these events are mutually exclusive events, using P(A)=0.23, and P(B)=0.73, what is P(B|A)?

# Question

The event that your uncle calls you on a Sunday is A and the event your sister calls you on a Tuesday is B. If these events are independent events, using P(A)=0.42, and P(B)=0.83, what is P(B|A)?

**Question**

Given the following information about events A and B:

- P(A)=1/12
- P(AAND B)=1/16
- P(A|B)=1/12

Are events A and B mutually exclusive, independent, both, or neither?

# Question

At a major international airport, passengers are questioned about their destination. Given Events A and B, are the two events mutually exclusive? Explain your answer.

Event A: The passengers are traveling to Paris, France.

Event B: The passengers are NOT traveling to Paris, France.

## Solution:

**Question**

The event of eating breakfast at a diner is A and the event of watching cable is B. If these events are independent events, using P(A)=0.22, and P(B)=0.46, what is P(B|A)?

**Correct answers:**

- $0.46

# Question

The event the number 9 car wins the race is A and the event the number 8 car wins the race is B. If these events are mutually exclusive events, using P(A)=0.39, and P(B)=0.31, what is P(A|B)?

**Correct answers:**

- 0

**Question**

The following information about undergraduates at a university is given:

- The probability that a randomly chosen undergraduate attends office hours is 24%;
- The probability that a randomly chosen undergraduate has a 30GPA or higher is 15.5%;
- The probability that a random chosen undergraduate has a 30GPA or higher given that they attend office hours is 12%.

Let event A is an undergraduate attending office hours and event B is an undergraduate having a 3.30 or higher GPA. Are events A and B mutually exclusive, independent, both, or neither?

### Correct answer:

Events A and B are neither independent nor mutually exclusive.

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