Often in buying a product at a supermarket, there is a concern about the item being underweight. Suppose there are 24 "one-pound" packages of frozen ground turkey on display and 2 of them are underweight. A consumer group buys 5 of the 24 packages at random. What is the probability of at least 1 of the 5 being underweight?

Question

Business

Clayton Griffin

23 May, 21:49

Often in buying a product at a supermarket, there is a concern about the item being underweight. Suppose there are 24 "one-pound" packages of frozen ground turkey on display and 2 of them are underweight. A consumer group buys 5 of the 24 packages at random. What is the probability of at least 1 of the 5 being underweight?

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Answers (1)

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Levy · Answer 1

The answer is: 38%

Explanation:

The probability of at least 1 of the 5 packages being underweight can be calculated using a technique known as hypergeometric distribution.

The probability of the first choice not being underweight is 22 out of 24, for the second choice it is 21 out of 23, for the third 20 out of 22, for the fourth 19 out of 21 and for the fifth 18 out of 20.

To find out the probability of at least one package being underweight, you must subtract the sum of the probabilities of not being underweight from 1 using the following formula:

1 - [ (22/24) x (21/23) x (20/22) x (19/21) x (18/20) ] =

1 - (0.91666667 x 0.91304348 x 0.90909091 x 0.9047619 x 0.9) =

1 - 0.62 = 0.38 or 38%