The probability of a bomb hitting a bridge is | vedclass

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Question

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

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(B) Let $n$ be the number of bombs dropped and $X$ be the number of bombs that hit the bridge. $X$ follows a binomial distribution $B(n, p)$ where $p = \frac{1}{2}$.The bridge is destroyed if $X \ge 2$. We want $P(X \ge 2) > 0.9$.This is equivalent to $1 - P(X  0.9$,which simplifies to $P(X $P(X We need $\frac{n + 1}{2^n} Testing values for $n$:For $n = 6$: $10(6 + 1) = 70$ and $2^6 = 64$. Since $70 > 64$,the condition does not hold.For $n = 7$: $10(7 + 1) = 80$ and $2^7 = 128$. Since $80 Thus,the least number of bombs required is $7$.

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

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