A couple uses a male condom correctly 85 % of the time and incorrectly 15 % 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
Expected pregnancies = 88; Pregnancies avoided with perfect use = 48
The correct answer is Expected pregnancies = 88; Pregnancies avoided with perfect use = 48 — Subtract to find pregnancies avoided: 88 − 40=48 pregnancies.
Step-by-step solution
- Write the proportion of correct use (0.85) and incorrect use (0.15).
- State the failure rates: perfect‑use = 0.02, typical‑use = 0.18.
- Calculate the weighted failure rate: (0.85 × 0.02)+(0.15 × 0.18)=0.017+0.027=0.044 (4.4 %).
- Multiply the weighted failure rate by the total couples: 0.044 × 2000=88 pregnancies expected under the given usage pattern.
- Calculate pregnancies if every couple used condoms perfectly: 0.02 × 2000=40 pregnancies.
- Subtract to find pregnancies avoided: 88 − 40=48 pregnancies.
Common mistake: Multiplying total couples by the typical‑use rate directly without weighting for correct and incorrect usage.
Concept tested: Contraceptive failure rate calculation
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