Question

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) 1

I had been asked this question in an international level competition.

The question is from Conditional Probability in chapter Probability of Mathematics – Class 12

Answer 1

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.