Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective?
A) 3/20 or 0.15
B) 3/17 or 0.176
C) ¼ or 0.25
D) 3/190 or 0.01579

Question

Quizplus · Accepted Answer

There are a total of 20 electric toothbrushes, and 3 of them are defective. Therefore, the probability that the first toothbrush sold is defective is 3/20. After one defective toothbrush has been sold, there are 2 defective toothbrushes left out of 19 toothbrushes. Therefore, the probability that the second toothbrush sold is also defective is 2/19. 
The probability that both events occur together (that the first two toothbrushes sold are defective) is the product of their probabilities, which is:
P(both defective) = (3/20) x (2/19) = 3/190, which is approximately 0.01579. 
Therefore, the answer is choice D.

Three Defective Electric Toothbrushes Were Accidentally Shipped to a Drugstore