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The probability of a bomb hitting a brid...

The probability of a bomb hitting a bridge is `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 :

Text Solution

Verified by Experts

The correct Answer is:
7
Let n be the least number of bombs required and X the number of bombs that hit the bridge. Then X follows a binomial distribution with parameter n and `p=1/2`
Now, `P(X ge 2) gt 0.9 rArr 1-P(X lt 2) gt 0.9`
`rArr P(X=0)+P(X=1) lt 0.1`
`rArr ""^(n)C_(0)(1/2)^(n)+""^(n)C_(1)(1/2)^(n-1) (1/2) lt 0.1 rArr 10(n+1) lt 2^(n)`
This gives ` n ge7`
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