Worksheet: Conditional Probability: Bayes’ Theorem

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

Q1:

Suppose that 𝐴 and 𝐡 are events with probabilities 𝑃(𝐴)=0.63 and 𝑃(𝐡)=0.77. Given that 𝑃(𝐡|𝐴)=0.88, find 𝑃(𝐴|𝐡).

Q2:

Suppose that 𝐴 and 𝐡 are events in a random experiment. Given that 𝑃(𝐴)=0.39 and 𝑃(𝐡|𝐴)=0.88, find π‘ƒο€Ίπ΅βˆ£π΄ο†.

Q3:

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

Determine the probability of 𝐴.

  • A29
  • B14
  • C12
  • D518
  • E16

Determine the probability of 𝐡.

  • A29
  • B12
  • C14
  • D518
  • E16

Determine the probability of (𝐴∣𝐡).

  • A13
  • B29
  • C118
  • D112
  • E38

Determine the probability of (𝐡∣𝐴).

  • A112
  • B38
  • C13
  • D14
  • E118

Is it true that 𝑃(𝐴)𝑃(𝐡∣𝐴)=𝑃(𝐴∩𝐡) and 𝑃(𝐡)𝑃(𝐴∣𝐡)=𝑃(𝐴∩𝐡)?

  • Ano
  • Byes

Q4:

Suppose that 𝐴 and 𝐡 are events with probabilities 𝑃(𝐴)=0.45 and 𝑃(𝐡)=0.7. Given that 𝑃(𝐡|𝐴)=0.84, find 𝑃(𝐴|𝐡).

Q5:

Suppose that 𝐴 and 𝐡 are events with probabilities 𝑃(𝐴)=0.4 and 𝑃(𝐡)=0.6. Given that 𝑃(𝐡|𝐴)=0.72, find 𝑃(𝐴|𝐡).

Q6:

Suppose that 𝐴 and 𝐡 are events in a random experiment. Given that 𝑃(𝐴)=0.36 and 𝑃(𝐡|𝐴)=0.75, find π‘ƒο€Ίπ΅βˆ£π΄ο†.

Q7:

Suppose that 𝐴 and 𝐡 are events in a random experiment. Given that 𝑃(𝐴)=0.45 and 𝑃(𝐡|𝐴)=0.66, find π‘ƒο€Ίπ΅βˆ£π΄ο†.

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