A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 40 that have no defects. What is the probability that at least one of the calculators is defective?

78.46% probability that at least one of the calculators is defective

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order that the calculators are chosen is not important. So we use the combinations formula to solve this problem.

Combinations formula:

The number of combinations of x elements from a set of n elements is given by:

What is the probability that at least one of the calculators is defective?

Either none of them are defective, or at least one is. The sum of these probabilities is 100%.

So

ND + A1D = 100

A1D = 100 - ND

In which ND is the probability that none are defective.

Probability that none are defective

Desired outcomes:

40 calculators have no defects, and 4 are going to be chosen

Total outcomes:

58 calculators in total, and 4 are going to be chosen

Probability:

21.54% probability that no calculators are defective, so ND = 21.54.

At least one defective:

A1D = 100 - ND = 100 - 21.54 = 78.46

78.46% probability that at least one of the calculators is defective

answer: what is the question you're trying to ask?

step-by-step explanation: