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Binomial distribution - Wikipedia, the free encyclopedia

Suppose that you throw n bombs. Each of them can only have 2 results (success = hitting the bridge with a probability p = 0.5, or failure with a probability q = 1-p = 0.5) and their results are independent.

The random variable X which counts the number of successes follows a binomial distribution

The number of k successes among the n shots is

Here this is a very specific case where p = 1-p

You can simplify the expression :

The number of 0 success among the n shots is

The number of 1 success among the n shots is

The number of successes higher than 2 among the n shots is

The minimum number of shots to get is 7

because for n=6 and for n=7