Two events A and B have PA 2 PB 3 a If PA given B8 what is P

Two events, A and B, have P(A)= .2, P(B)= .3. a) If P(A given B)=.8, what is P(A union B)? b) If P(AUB)=.4, what is P(A given B)?

Solution

a)

P(A U B) = P(A) + P(B) - P(A|B) P(B)

Thus,

P(A U B) = 0.2 + 0.3 - 0.8*0.3 = 0.26 [ANSWER]

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b)

P(A U B) = P(A) + P(B) - P(A|B) P(B)

0.4 = 0.2 + 0.3 - P(A|B)*0.3

P(A|B) = 0.3333333 [ANSWER]