Let A and B , be two events such that the probability that exactly one of them occurs is (2)/(5) , and the probability that A or B , occurs is (1)/(2) , then the probability of both of them occur together is.

Correct answer: D. 0.10 P (exactly one) = (2)/(5) = P(A) + P(B) - 2P(A B) = (2)/(5) . . . (1) P(A B) = (1)/(2) = P(A) + P(B) - P(A B) = (1)/(2) . . . (2) ∴ P(A B) = (1)/(2) - (2)/(5) = (5 - 4)/(10) = (1)/(10) .

JEE Main 20208 JanuaryEvening Shift

Exam: JEE Main
Year: 2020
Date: 8 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Probability

JEE Main 2020 · 8 January · Evening Shift · Mathematics · Probability

Let A and B , be two events such that the probability that exactly...

Let

A

and

B

, be two events such that the probability that exactly one of them occurs is

\dfrac{2}{5}

, and the probability that

A

B

, occurs is

\dfrac{1}{2}

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

Options

A $0.02$
B $0.20$
C $0.01$
D $0.10$

Correct answer

D. $0.10$

Step-by-step solution

P

(exactly one)

= \dfrac{2}{5}

= P\left(A\right) + P\left(B\right) - 2P\left(A \cap B\right) = \dfrac{2}{5} . . . \left(1\right)

P\left(A \cup B\right) = \dfrac{1}{2}

= P\left(A\right) + P\left(B\right) - P\left(A \cap B\right) = \dfrac{1}{2} . . . \left(2\right)

∴ P\left(A \cap B\right) = \dfrac{1}{2} - \dfrac{2}{5} = \dfrac{5 - 4}{10} = \dfrac{1}{10}

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