Suppose a biological cell contains 400 genes. when treated radioactively the probability that
a gene will change into mutant gene is 0.006 and is independent of the other genes. what is
the approximate probability that there are at most 4 mutant genes after the treatment?

Let be the random variable representing the number of genes that do get mutated. Here denotes a binomial distribution with parameters (total number of genes) and (probability of mutation).

Then the probability that *at most* 4 genes get mutated is



where



You should find that

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