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.

• 0.44
• 0.46
• 0.48
• 0.5
• 0.52

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]]