JEE Advanced 2020 · Paper 2 · Mathematics Q2

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MathematicsInteger+3 / -1Question 38 of 54

The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is ______

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Answer and worked solution

Official answer: 6

We need $P(X\ge3)\ge0.95$ , where $X\sim\text{Bin}(n,\frac34)$ . Equivalently $P(X\le2)\le0.05$ , with
$P(X\le2)=\frac{1+3n+9\binom n2}{4^n}.$

$n=5$ : $\dfrac{1+15+90}{1024}=0.1035$ . Too big.
$n=6$ : $\dfrac{1+18+135}{4096}=0.0376\le0.05$ . ✓

Answer: 6

Topics:Independent events Classical probability

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JEE Advanced 2020 · Paper 2, Mathematics question 2