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, neither will be returned for a refund.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
(1-.05)(1-.05) = ?
To find the probability that neither of the two items sold will be returned for a refund, we need to first calculate the probability that one item is not returned, and then multiply that probability by itself for the second item.
Given that five percent of all items sold are returned, the probability of one item not being returned is 1 minus the probability of it being returned.
Probability of one item not being returned = 1 - 0.05 = 0.95
Since the two items are being sold independently, we multiply the probabilities together to find the probability that both items are not returned:
Probability that both items are not returned = 0.95 * 0.95 = 0.9025
Therefore, the probability that neither of the two items sold during a given hour will be returned for a refund is 0.9025 or 90.25%.