The probability of a bomb hitting a bridge is | vedclass

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Question

(D) Let $n$ be the number of bombs dropped. Let $X$ be the number of bombs that hit the bridge. $X$ follows a binomial distribution $B(n, p)$ where $p

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(D) Let $n$ be the number of bombs dropped. Let $X$ be the number of bombs that hit the bridge. $X$ follows a binomial distribution $B(n, p)$ where $p = 1/2$.The bridge is destroyed if there are at least $2$ hits,i.e.,$X \geq 2$.We want $P(X \geq 2) > 0.9$.This is equivalent to $1 - P(X  0.9$,which means $P(X $P(X So,we need $\frac{n+1}{2^n} Testing values for $n$:For $n=7$: $10(7+1) = 80$ and $2^7 = 128$. Since $80 For $n=6$: $10(6+1) = 70$ and $2^6 = 64$. Since $70 > 64$,this does not work.Wait,checking the inequality again: $10(n+1)  0.9$.

The probability of a bomb hitting a bridge is $1/2$ and two direct hits are needed to destroy it. Find the least number of bombs required so that the probability of the bridge being destroyed is greater than $0.9$.

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