Question

A manufacturing machine has a 10% defect rate. If 7 items are chosen at random, what is the probability that at least one will have a defect? (Round your answer to 4 decimal places)

A) 0.0057
B) 0.0960
C) 0.9993
D) 0.9038

Answer 1

To find the probability that at least one item will have a defect, subtract the probability of no item having a defect from 1.

Step-by-step explanation:

To find the probability that at least one item will have a defect, we can use the complement rule. The complement of at least one item having a defect is no item having a defect. So, the probability of no item having a defect is equivalent to 1 minus the probability of at least one item having a defect.

The probability of no item having a defect is (1-0.1)^7 = 0.9^7 = 0.4783.

Therefore, the probability that at least one item will have a defect is 1 - 0.4783 = 0.5217.