The number of bombs that should be dropped to give a 99% chance or better of completely destroying the target can be 11, 12, and 13.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
The probability of success in one strike is p = 1/2
The probability of failure will be:
q = 1/2
Now, the probability of a successes P( x = a ) = ₙCᵃ × ( 1/2 )ᵃ × ( 1/2 )ⁿ ⁻ ᵃ
P( x = a ) = ₙCᵃ ( 1/2 )ⁿ
According to the given condition,
P( x ≥ 2 ) ≥ 0.99
= 1 − P( x < 2 ) ≥ 0.99
= 1 − P( x = 0 ) − P( x = 1 ) ≥ 0.99
= 1 − 0.99 ≥ ( 1 + n)/2ⁿ
= 2ⁿ ≥ 100 + 100n
When n = 10, 2ⁿ < 100 + 100n
For n = 11, 12, 13, 2ⁿ > 100 + 100n
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