JEE Main 2022 · 28 Jul · Shift 2 · Mathematics Q79

MathematicsSingle correct+4 / -1Question 79 of 90

Let A and B be two events such that $P(B|A)=\dfrac25$ , $P(A|B)=\dfrac17$ and $P(A\cap B)=\dfrac19$ . Consider

(S1) $P(A'\cup B)=\dfrac56$ ,

(S2) $P(A'\cap B')=\dfrac1{18}$

Then

Both (S1) and (S2) are true

Both (S1) and (S2) are false

Only (S1) is true

Only (S2) is true

Answer and worked solution

Official answer: A

Probabilities. $P(A)=\frac5{18}$ , $P(B)=\frac79$ .

(S1). $1-P(A\cap B')=1-\frac3{18}=\frac56$ . (S2). $1-P(A\cup B)=1-\frac{17}{18}=\frac1{18}$ . Both true.

(A)

Topics:Conditional probability

JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 79