Question

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?

Group of answer choices

0.802

0.150

0.184

Answer 1

We have :

Total calculators = 15 + 30 = 45

Probability of a defective calculator = 15/45 = 1/3

Probability of a non-defective calculator = 30/45 = 2/3

We have 4 calculators selected out of 45

Let X denote the number of defective calculators chosen

Probability that at least one of the calculators is defective = 1 - Probability that none of the calculators is defective

Now,

Probability that none of the calculators is defective = Probability that all 4 calculators are non-defective =

= ( Probability of a non-defective calculator )⁴ = (2/3)⁴ = 0.198

So,

Probability that at least one of the calculators is defective = 1 - 0.198 = 0.802

Correct option : 0.802