# Worksheet: Bayes' Theorem

In this worksheet, we will practice computing probabilities using Bayes' rule.

**Q1: **

Suppose that and are events with probabilities and . Given that , find .

**Q2: **

Suppose that and are events in a random experiment. Given that and , find .

**Q3: **

Sameh rolls two fair dice numbered from one to six and records the results. Let be the event of rolling two numbers whose product is a square number and let be the event of rolling two numbers that are even.

Determine the probability of .

- A
- B
- C
- D
- E

Determine the probability of .

- A
- B
- C
- D
- E

Determine the probability of ).

- A
- B
- C
- D
- E

Determine the probability of .

- A
- B
- C
- D
- E

Is it true that and ?

- Ayes
- Bno

**Q4: **

Suppose that and are events with probabilities and . Given that , find .

**Q5: **

Suppose that and are events with probabilities and . Given that , find .

**Q6: **

Suppose that and are events in a random experiment. Given that and , find .

**Q7: **

Suppose that and are events in a random experiment. Given that and , find .