Question

The probability of a bomb hitting a target is 1/2. the least number of bombs that should be dropped to ensure that probability of the target getting bombed is at least 0.9 is

Answer 1

probability of hitting the target = p = 1/2
probability of missing the target = q = 1/2

Probability of hitting the target in n droppings or n bombs = P(n).

P(n = 1) = 1/2

P(n = 2) = P(n = 1) + q * p
              = 1/2 + 1/2 * 1/2 = 3/4

P(n = 3) = P(n= 2) + q² p
                = 3/4 + 1/8 = 7/8 = 0.87

P(n = 4) = P(n=3) + q³ p
              = 7/8 + 1/16 = 15/16 > 0.9

So the minimum number of bombs to be dropped are = 4.

Answer 2

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