QJEEM20Ma0327: JEE Main 2020 Mathematics - Class 12 JEEM20Ma0327 Solution: Let A and B be two events such that the probability that…

Question

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Let A and B be two events such that the probability that exactly one of them occurs is

{2 \over 5}

and the probability that A or B occurs is

{1 \over 2}

, then the probability of both of them occur together is :

Accepted Answer

Probability that exactly one of them occurs

P(A) + P(B) – 2P (A

\cap

B) =

{2 \over 5}

.....(1)

Probability that A or B occurs is

P(A) + P(B) – P(A

\cap

B) =

{1 \over 2}

......(2)

Doing (2) - (1)

P(A

\cap

B) =

{1 \over 2} - {2 \over 5}

= 0.10

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