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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

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Solution

Let n is total no. of bombs being dropped.
At least 2 bombs should hit.
Probability0.99
p(x2)0.99
1p(x<2)0.99
1(p(x=0)+p(x=1))0.99
1[nC0p0qn+nC1p1qn1]0.99
1[qn+pnqn1]0.99
1[12n+n2×12n1]0.99
0.0112n(n+1)
2n100+100n
2n100n100
n11

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