Five percent of all items sold by a mail-order company are returned by customers for a refund. Find the probability that of two items sold during a given hour by this company both will be returned for a refund (round to four decimal places).
It's just 0.05 x 0.05 = 0.0025. The fact that they were both sold during a given hour is irrelevant to the calculation, BUT you're assuming when you perform that calculation that the returning of one item is independent of whether or not another one is returned. Given that they were both sold within such a small interval of time, you might feel the need to question that assumption.
To find the probability that both items will be returned for a refund, we need to multiply the probability of one item being returned by itself.
Given that five percent of all items are returned, the probability of one item being returned is 0.05.
Therefore, the probability of both items being returned is:
P(both items returned) = P(item 1 returned) * P(item 2 returned)
P(both items returned) = 0.05 * 0.05 = 0.0025
So, the probability that both items sold during a given hour by this company will be returned for a refund is 0.0025 or 0.25%.