Question

A box contains 32 parts, of which 5 are defective and 27 are nondefective. 2 parts are selected without replacement. Find the probability P (both are defective).

Answer 1

To find the probability that both selected parts are defective, multiply the probability of selecting one defective part by the probability of selecting another defective part from the remaining parts.

Step-by-step explanation:

To find the probability that both selected parts are defective, we need to calculate the probability of selecting one defective part and then the probability of selecting another defective part from the remaining parts.

P(both are defective) = P(first part is defective) * P(second part is defective given the first part is defective)

P(first part is defective) = number of defective parts / total number of parts = 5 / 32

P(second part is defective given the first part is defective) = number of defective parts - 1 / total number of remaining parts - 1 = 4 / 31

P(both are defective) = (5 / 32) * (4 / 31) = 20 / 992