Let A and B be two events such that P(B∖A) = 2/5, P(A∖B) = 1/7 and P(A B) = 1/9. Consider (S1) P(A' B) = 5/6, (S2) P(A' B') = 1/18. Then

JEE Main 2022 Mathematics question

Let A and B be two events such that P(B∖A) = 2/5, P(A∖B) = 1/7 and P(A B) = 1/9. Consider (S1) B) = 5/6, (S2) . Then

(1)Both (S1) and (S2) are trueCorrect
(2)Both (S1) and (S2) are false
(3)Only (S1) is true
(4)Only (S2) is true

Answer: (1)

Solution

The printed working reads the data as P(B|A) = 2/5 and P(A|B) = 1/7 (conditional probabilities). Then P(A|B) = P(A B)/P(B) = 1/7 gives P(B) = 7/9, and P(B|A) = P(A B)/P(A) = 2/5 gives P(A) =

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Question ID VK-034704