Five percent of all items sold by 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,
a) both will be returned for a refund
b) neither will be returned for a refund
The probability of both/all events occurring is found by multiplying the probabilities of the individual events.
a) .05*.05 = ?
b) (1-.05)(1-.05) = ?
a) 0.0025
b)0.9025
Seven 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.
a) Well, if five percent of all items sold by the company are returned for a refund, then the probability of one item being returned is 0.05. Since the events are independent (one item being returned doesn't affect the other item), we can multiply the probabilities together. So, the probability that both items will be returned for a refund is:
0.05 * 0.05 = 0.0025
So, the probability that both items will be returned for a refund is 0.0025 or 0.25%. That's quite low! They must be selling some quality stuff!
b) If five percent of items are returned, that means 95% of items are not returned. So, the probability of one item not being returned is 0.95. Since the events are independent, we can multiply the probabilities together. So, the probability that neither item will be returned for a refund is:
0.95 * 0.95 = 0.9025
So, the probability that neither item will be returned for a refund is 0.9025 or 90.25%. Looks like most customers are happy with their purchases!
To find the probability in both cases, we'll need to use the concept of probability and apply it to the given scenario.
a) Probability that both items will be returned for a refund:
Let's break down the problem. We know that the probability of one item being returned for a refund is 5% or 0.05. Since there are two items, we need to multiply the probability twice.
P(both returned) = P(returned) * P(returned)
P(both returned) = 0.05 * 0.05
P(both returned) = 0.0025
Therefore, the probability that both items will be returned for a refund is 0.0025 or 0.25%.
b) Probability that neither item will be returned for a refund:
If the probability of one item being returned for a refund is 5% or 0.05, then the probability of an item not being returned for a refund is the complement of that, which is 1 - 0.05 = 0.95.
P(neither returned) = P(not returned) * P(not returned)
P(neither returned) = 0.95 * 0.95
P(neither returned) = 0.9025
Therefore, the probability that neither item will be returned for a refund is 0.9025 or 90.25%.