Let A and B be two events such that
P (A) = 0.5, P (B) = 0.3, and P(A|B)=0.5,
Then P(AC∣∣BC) equals
A
0.5
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B
0.6
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C
0.15
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D
0.3
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Solution
The correct option is A 0.5 GivenP(A)=0.5,P(B)=0.3andP(A|B)=0.5WeknowthatP(A|B)=P(A∩B)P(B)∴P(A∩B)=P(A|B)×P(B)=0.5×0.3=0.15 Now,P(AC∣∣BC)=P(AC∩BC)P(BC)=P(A∪B)CP(BC)=1−P(A∪B)1−P(B)=1−{P(A)+P(B)−P(A∩B)}1−P(B)=1−(0.5+0.3−0.15)0.7=0.350.7=0.5