# Worksheet: Conditional Probability: 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:

Matthew 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 .

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Determine the probability of .

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Determine the probability of ).

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Determine the probability of .

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Is it true that and ?

• Ano
• Byes

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 .