1.

If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________(a) 3/5(b) 2/3(c) 1/2(d) 1I had been asked this question in an international level competition.The question is from Conditional Probability in chapter Probability of Mathematics – Class 12

Answer» RIGHT option is (d) 1

Explanation: We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional PROBABILITY)

ALSO P(A∪B) = P(A)+P(B) – P(A∩B). (By formula of probability)

\(\RIGHTARROW\) 8/11 = 7/11 + 6/11 – P(A∩B)

\(\Rightarrow\) P(A∩B) = 13/11 – 7/11

\(\Rightarrow\) P(A∩B) = 6/11

P(A|B) = (6/11) / (6/11).

P(A|B) = 1.


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