IIT-JEE 2012 · Paper 2 · Mathematics Q58

MathematicsMultiple correct+4Question 58 of 60

Let $X$ and $Y$ be two events such that $P(X|Y)=\dfrac12$ , $P(Y|X)=\dfrac13$ and $P(X\cap Y)=\dfrac16$ . Which of the following is (are) correct?

P(X\cup Y)=\dfrac23

X

and

Y

are independent

X

and

Y

are not independent

P(X^c\cap Y)=\dfrac13

Answer and worked solution

Official answer: A, B

Probabilities. $P(Y)=\dfrac{P(X\cap Y)}{P(X\mid Y)}=\dfrac13$ and $P(X)=\dfrac{P(X\cap Y)}{P(Y\mid X)}=\dfrac12$ .

(A), (B)

Topics:Conditional probability Independent events

IIT-JEE 2012 · Paper 2, Mathematics question 58