JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q86

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MathematicsSingle correct+4 / -1Question 86 of 90

For three events A, B and C,

P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = $\dfrac14$ and P(All the three events occur simultaneously) = $\dfrac1{16}$ .

Then the probability that at least one of the events occurs, is :

\dfrac7{16}

\dfrac7{64}

\dfrac3{16}

\dfrac7{32}

Answer and worked solution

Official answer: A

$P(\text{exactly one of A, B})=P(A)+P(B)-2P(AB)$ . Adding the three equations:
$\sum P(A)-\sum P(AB)=\frac38.$
So $P(A\cup B\cup C)=\frac38+\frac1{16}=\frac7{16}$ .

Topics:Classical probability Sets and operations

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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 86