Question

A supplier delivers an order for 20 electric toothbrushes to a store. by accident, three of the electric toothbrushes are defective. what is the probability that the first two electric toothbrushes sold will be returned because they are defective?

Answer 1

3 of the 20 toothbrushes are defective, so the initial probability of selecting a defective toothbrush on the first try is 3/20. After that, there will be 2 defective toothbrushes in the remaining 19, so the probability of selecting one of those on the 2nd try will be 2/19. To get the probability of those two events happening sequentially, we multiply the two probabilities. Thus (3/20)*(2/19) = 6/380 = 0.0157, or about 1.6%.