A manufactured lot of buggy whips has 20 items, of which 5 are defective. A random sample of 5 items is chosen to be inspected. Find the probability that the sample contains exactly one defective item if the sampling is done without replacement.

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: A

The number of ways choosing 5 items with exactly one defective item equals

[[math]]5 \binom{15}{4}[[/math]]

out of a total of [math]\binom{20}{5}[/math] ways of choosing 5 items. Hence the probability equals

[[math]] \frac{5 \binom{15}{4}}{\binom{20}{5}} = 0.4402. [[/math]]