Question

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.

Answer 1

The probability of both items being returned for a refund by a mail-order company, when 5% of items are typically returned, is found by multiplying the probability of each independent event, resulting in a combined probability of 0.25% or 0.0025.

Step-by-step explanation:

To find the probability that two items sold by a mail-order company will both be returned for a refund, we must consider each sale as an independent event. Given that 5% of items, or 0.05 as a probability, are returned, we're looking for the probability of both events happening back-to-back. Therefore, we multiply the individual probabilities:

Probability of first item being returned = 0.05
Probability of second item being returned = 0.05

To find the combined probability of both items being returned, we multiply the two probabilities:

P(both items returned) = 0.05 × 0.05 = 0.0025.

So, the probability that both items sold during a given hour will be returned for a refund is 0.0025, or 0.25%.

Answer 2

The probability that both of the two items sold by the mail-order company will be returned is 0.25%, found by multiplying the probability of one item being returned (5% or 0.05) by itself since both events are considered independent.

Step-by-step explanation:

The question is asking to calculate the probability that both of two items sold during a given hour by a mail-order company will be returned for a refund, given that 5% of items are returned on average. To find this, we assume the events are independent and multiply the probability of one event happening by itself since both events have to happen back-to-back.

The probability of one item being returned is 5% or 0.05. Therefore, the probability that both items are returned would be 0.05 × 0.05 which equals 0.0025 or 0.25%. Thus, there is a 0.25% chance that both of the items will be returned for a refund.