B1 B2 B3 B4 A 009 022 015 020 Ac 003 010 009 012 What is the

B₁

B₂

B₃

B₄

A

0.09

0.22

0.15

0.20

A^c

0.03

0.10

0.09

0.12

What is the probability that A occurs?

What is the probability that B₂ occurs?

What is the probability that A^c and B₄ occur?

What is the probability that A or B₃ occurs?

Given that B₂ has occurred, what is the probability that A occurs?

Given that A has occurred, what is the probability that B₄ occurs?

Solution

a)

P(A) = 0.09+0.22+0.15+0.20 = 0.66 [ANSWER]
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b)

P(B2) = 0.22+0.10 = 0.32 [ANSWER]

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c)

P(Ac and B4) = 0.12 [ANSWER]

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d)

P(A or B3) = 0.09+0.22+0.15+0.20+0.09 = 0.75 [ANSWER]

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e)

P(A|B2) = 0.22/(0.22+0.10) = 0.6875 [ANSWER]

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f)

P(B4|A) = 0.20/(0.09+0.22+0.15+0.20) = 0.303030303 [ANSWER]