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Question

In a precision bombing attack, there is a 50% chance that any one bomb will strike the target. Two direct hits are required to destroy the target completely. The number of bombs which should be dropped to give a 99% chance or better of completely destroying the target can be

A
12
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B
11
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C
10
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D
13
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Solution

The correct options are
A 12
B 11
C 13
The probability of success in one strike is p=12.
Probability of failure =q=12
Now, probability of r successes P(x=r)=nCr.(12)r.(12)nr=nCr(12)n
According to the given condition, P(x2)0.99
1P(x<2)0.99
1P(x=0)P(x=1)0.99
10.991+n2n
2n100+100n
For n=10, 2n<100+100n
For n=11,12,13,
2n>100+100n.

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