In a community of 1500 couples, 80 % of couples use male condoms correctly and 20 % incorrectly. The perfect‑use failure rate of condoms is 1.5 % per year and the typical‑use failure rate is 15 % per year.
Answer
63 pregnancies expected; 41 pregnancies avoided
The correct answer is 63 pregnancies expected; 41 pregnancies avoided — Pregnancies avoided = (63 - 22.5 = 40.5) ≈ 41.
Step-by-step solution
- Compute weighted failure probability: - Correct use: (0.8 \times 0.015 = 0.012). - Incorrect use: (0.2 \times 0.15 = 0.03). - Total weighted failure = (0.012 + 0.03 = 0.042).
- Multiply by number of couples for expected pregnancies: (1500 \times 0.042 = 63).
- If all couples used condoms perfectly, failure = (0.015 \times 1500 = 22.5) ≈ 22.
- Pregnancies avoided = (63 - 22.5 = 40.5) ≈ 41.
Common mistake: Using the same failure rate for all couples instead of weighting by correct/incorrect usage
Concept tested: Weighted contraceptive failure rate
Published · How this solution was prepared and checked
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