JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q86

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MathematicsSingle correct+4 / -1Question 86 of 90

Let E and F be two independent events. The probability that both E and F happen is $\dfrac1{12}$ and the probability that neither E nor F happens is $\dfrac12$ , then a value of $\dfrac{P(E)}{P(F)}$ is :

\dfrac43

\dfrac32

\dfrac13

\dfrac5{12}

Answer and worked solution

Official answer: A

$pq=\frac1{12}$ and $(1-p)(1-q)=\frac12$ , so $p+q=\frac7{12}$ . Then $p$ and $q$ are the roots of $12t^2-7t+1=0$ : $\frac13$ and $\frac14$ . So $\frac{P(E)}{P(F)}=\frac43$ is a possible value.

Topics:Independent events

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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 86