Question

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 five 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.

Answer 1

The probability that at least one out of five randomly selected PIN codes will have repeating digits is 0.703.

Step-by-step explanation:

In this case, we want to find the probability that at least one out of five randomly selected PIN codes will have repeating digits. We can use the complement rule to find this probability. The complement of having at least one PIN code with repeating digits is having none of the PIN codes with repeating digits. So, we need to find the probability that none of the five PIN codes have repeating digits.

The probability of a PIN code not having repeating digits is 1 minus the probability of a PIN code having repeating digits. The probability of a PIN code having repeating digits is given as 17.8%, which can be written as 0.178. Therefore, the probability of a PIN code not having repeating digits is 1 - 0.178 = 0.822.

Since each of the five PIN codes is selected randomly and independently, we can multiply the probabilities together to find the probability that none of them have repeating digits: 0.822 * 0.822 * 0.822 * 0.822 * 0.822 = 0.297.

Finally, we can subtract this probability from 1 to find the probability that at least one out of the five PIN codes will have repeating digits: 1 - 0.297 = 0.703.

Answer 2

To calculate the probability, find the probability that none of the five people have repeating digits and subtract it from 1.

Step-by-step explanation:

To calculate the probability that at least one of the five people will have repeating digits in their PIN code, we can calculate the probability that none of them have repeating digits and subtract it from 1.

The probability that one person does not have repeating digits is 1 - 0.178 = 0.822. So, the probability that none of the five people have repeating digits is 0.822^5 = 0.4674.

Therefore, the probability that at least one of the five people will have repeating digits is 1 - 0.4674 = 0.5326, rounded to four decimal places.