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Lesson: Bayes's Rule

Worksheet • 7 Questions

Q1:

Suppose that 𝐴 and 𝐡 are events with probabilities 𝑃 ( 𝐴 ) = 0 . 6 3 and 𝑃 ( 𝐡 ) = 0 . 7 7 . Given that 𝑃 ( 𝐡 | 𝐴 ) = 0 . 8 8 , find 𝑃 ( 𝐴 | 𝐡 ) .

Q2:

Suppose that 𝐴 and 𝐡 are events with probabilities 𝑃 ( 𝐴 ) = 0 . 4 5 and 𝑃 ( 𝐡 ) = 0 . 7 . Given that 𝑃 ( 𝐡 | 𝐴 ) = 0 . 8 4 , find 𝑃 ( 𝐴 | 𝐡 ) .

Q3:

Suppose that 𝐴 and 𝐡 are events with probabilities 𝑃 ( 𝐴 ) = 0 . 4 and 𝑃 ( 𝐡 ) = 0 . 6 . Given that 𝑃 ( 𝐡 | 𝐴 ) = 0 . 7 2 , find 𝑃 ( 𝐴 | 𝐡 ) .

Q4:

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 .

  • A 2 9
  • B 1 2
  • C 1 6
  • D 5 1 8
  • E 1 4

Determine the probability of 𝐡 .

  • A 1 4
  • B 1 2
  • C 2 9
  • D 5 1 8
  • E 1 6

Determine the probability of ( 𝐴 ∣ 𝐡 ).

  • A 1 3
  • B 2 9
  • C 1 1 2
  • D 1 1 8
  • E 3 8

Determine the probability of ( 𝐡 ∣ 𝐴 ) .

  • A 3 8
  • B 1 4
  • C 1 1 2
  • D 1 1 8
  • E 1 3

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

  • Ano
  • Byes

Q5:

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

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