JEE PYQ: Probability Question 22
Question 22 - 2020 (05 Sep Shift 2)
In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is ______.
Show Answer
Answer: 11
Solution
$1 - {}^nC_0\left(\frac{1}{2}\right)^n - {}^nC_1\left(\frac{1}{2}\right)^n \geq 0.99$. $\frac{n+1}{2^n} \leq \frac{1}{100}$. $2^n \geq 100(n+1)$. For $n = 11$: $2^{11} = 2048 \geq 1200$. So $n \geq 11$.
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