A production process is known to produce a particular item in such a way that 5 percent of these are defective.If two items are randomly selected as they come off the production line,what is the probability that both are defective (assuming that they are independent)?
A)0.0100
B)0.1000
C)0.2000
D)0.0025
E)0.0250

Question

Quizplus · Accepted Answer

Since the items are independent, the probability of both being defective can be found by multiplying the probability of one item being defective by the probability of the other item being defective, given that the first was defective.

So, P(both defective) = P(first was defective) x P(second was defective given that the first was defective)

P(first was defective) = 0.05 
Since there is one defective item among all items, the probability of selecting another defective item from the remaining ones is 4/99

P(second was defective given that the first was defective) = 4/99

P(both defective) = 0.05 x 4/99 
= 0.0025

Therefore, the probability that both items are defective is 0.0025 or 0.25%. The answer is D.

A Production Process Is Known to Produce a Particular Item