1help with stat hwSolutiona PA PE1 PE2 PE3 08 answer PB

Solution

a)

P(A) = P(E1) + P(E2) + P(E3) = 0.8 [answer]

P(B) = P(E2) + P(E3) + P(E5) = 0.6 [answer]

P(A and B) = P(E2) + P(E3) = 0.5 [answer]

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b)

P(E1|A) = P(E1) / P(A) = 0.3/0.8 = 0.375 [answer]

As

P(E1):P(E2):P(E3) = 0.3:0.2:0.3

Multiplying all by 10,

P(E1):P(E2):P(E3) = 3:2:3 [ANSWER]

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As E1, E2, and E3 are simply subsets of A, then their ratio remains the same, even when given A:

P(E1|A):P(E2|A):P(E3|A) = 3:2:3 [ANSWER]

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c)

P(B|A) = P(A and B) / P(A) = 0.5/0.8 = 0.625 [answer]