If P(A)=0.4, P(B)=0.5 and P (B/A)=0.8, find the following probabilities: a.) P(A

Question

If P(A)=0.4, P(B)=0.5 and P (B/A)=0.8, find the following probabilities: a.) P(AnB) b.) P(AuB) c.) P(A|B). A company has two vacancies at the junior executive level. Ten people, seven men and three women, are eligible and equally qualified. The company has decided to draw two names at random from the list of eligibles. What is the probability that: a.) both positions will be filled by women? b.) at least one of the positions will be filled by a woman? c.) neither of the positions will be filled by a woman?

Explanation / Answer

P(A) = 0.4

P(B) = 0.5

P(B/A) = P( A INTERSECTION B ) / P(A) = 0.8

A) P(A INTERSECTION B) = 0.8*P(A) = 0.8*0.4 = 0.32

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

P(A U B) = 0.4 + 0.5 - 0.32 = 0.58

C) P(A/B) = P(A INTERSECTON B) / P(B) = 0.32/0.5 = 0.64

2ND)

TOTAL PEOPLE = 10

MEN PROBABILITY = 7/10 = 0.7

WOMEN PROBABILITY = 0.3

A) BOTH FILLED BY WOMEN = 0.3^2 = 0.09

B)AT LEAST ONE WOMEN = 2C1*(0.3)^1*(0.7)^1 + 0.09 = 0.51

C) MEITHER POSITION FILLED BY WOMEN = 0.7^2 = 0.49

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