Enter your PIN: The technology company DataGenetics suggests that 17.8 % of all four-digit personal identification...

Enter your PIN: The technology company DataGenetics suggests that 17.8 % of all four-digit personal identification numbers, or PIN codes, have a repeating digits format such as 2525. Assuming this to be true, if the PIN codes of nine people are selected at random, what is the probability that at least one of them will have repeating digits? Round your answer to four decimal places. The probability that at least one of the codes will have repeating digits is

Expert Solution

Solution: Let x be the number of codes having repeating digits. Then the random variable x follows the binomial distribution with n = 9 and p = 0.178.

We are required to find:

We know that:

Now using the binomial probability formula, we have:

Therefore, the probability that at least one of the codes will have repeating digits is 0.8287

orchestra answered 2 years ago

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