A couple uses a male condom correctly 80 % of the time and incorrectly 20 % of the time. The perfect‑use failure rate of condoms is 2 % per year and the typical‑use failure rate is 18 % per year. If 2000 couples use condoms for one year, calculate (a) the expected number of unintended pregnancies and (b) the number of pregnancies that could have been avoided if all couples had used condoms perfectly.
Answer
104 64
The correct answer is 104 64 — Pregnancies avoided = 104 − 40 = 64.
Step-by-step solution
- Weighted failure rate = 0.8 × 2 % + 0.2 × 18 % = 5.2 %.
- Expected pregnancies = 2000 × 0.052 = 104.
- Pregnancies with perfect use = 2000 × 0.02 = 40.
- Pregnancies avoided = 104 − 40 = 64.
Common mistake: Using the typical‑use rate directly without weighting for correct/incorrect usage
Concept tested: Condom failure rates
Published · How this solution was prepared and checked
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