In a population of 300 women using both combined oral contraceptive pills (typical‑use failure rate 9 % per year) and male condoms (typical‑use failure rate 18 % per year) over one year, assuming failures of the two methods are independent, what is the expected number of pregnancies among the women?
Answer
76
The correct answer is 76 — Rounded to nearest whole number gives 76 pregnancies.
Step-by-step solution
- Probability of success with pill = 1 − 0.09 = 0.91.
- Probability of success with condom = 1 − 0.18 = 0.82.
- Probability both succeed = 0.91 × 0.82 = 0.7462.
- Probability of pregnancy = 1 − 0.7462 = 0.2538.
- Expected pregnancies = 300 × 0.2538 ≈ 76.
- Rounded to nearest whole number gives 76 pregnancies.
Common mistake: Adding failure rates instead of computing complement
Concept tested: Combined contraceptive efficacy
Published · How this solution was prepared and checked
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