A sample of 4 different calculators is randomly selected from a group containing 15 that are defective and 30 that have no defects. What is the probability that at least one of the calculators is defective?
A)0.150
B)0.184
C)0.816
D)0.802

Question

Quizplus · Accepted Answer

The probability of selecting at least one defective calculator is easier to calculate by finding the complement, which is the probability of selecting no defective calculators at all, and then subtracting that from 1. The probability of selecting 4 non-defective calculators from the 30 available is (30/45) * (29/44) * (28/43) * (27/42). The complement of this probability gives the probability of selecting at least one defective calculator: 1 - [(30/45) * (29/44) * (28/43) * (27/42)] = 0.816.

A Sample of 4 Different Calculators Is Randomly Selected from a Group