IIT-JEE 2011 · Paper 2 · Mathematics Q50

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MathematicsMultiple correct+4Question 50 of 60

Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\dfrac{11}{25}$ and the probability of none of them occurring is $\dfrac2{25}$ . If $P(T)$ denotes the probability of occurrence of the event $T$ , then

P(E)=\frac45

P(F)=\frac35

P(E)=\frac15

P(F)=\frac25

P(E)=\frac25

P(F)=\frac15

P(E)=\frac35

P(F)=\frac45

Answer and worked solution

Official answer: A, D

Let $P(E)=p$ , $P(F)=q$ , both independent:
$p+q-2pq=\frac{11}{25},\qquad(1-p)(1-q)=\frac2{25}\iff1-(p+q)+pq=\frac2{25}.$

Solve. Adding, $1-pq=\frac{13}{25}$ , so $pq=\frac{12}{25}$ and $p+q=\frac75$ . Then $p$ and $q$ are $\frac45$ and $\frac35$ in some order.

(A), (D)

Topics:Independent events

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IIT-JEE 2011 · Paper 2, Mathematics question 50