A group of 1000 women uses both combined oral contraceptive pills (typical‑use failure 9 % per year) and male condoms (typical‑use failure 18 % per year) simultaneously over one year, assuming failures of the two methods are independent. How many pregnancies are expected? How many pregnancies would be expected if they used only oral contraceptive pills? What is the reduction in expected pregnancies due to dual use?
Answer
254 pregnancies expected; 90 pregnancies if only oral contraceptives; 164 pregnancies avoided due to dual use
The correct answer is 254 pregnancies expected; 90 pregnancies if only oral contraceptives; 164 pregnancies avoided due to dual use — Reduction due to dual use: 254 − 90 = 164.
Step-by-step solution
- Determine probability of no pregnancy from OCP: 1 − 0.09 = 0.91.
- Determine probability of no pregnancy from condom: 1 − 0.18 = 0.82.
- Assuming independence, probability of no pregnancy from both: 0.91 × 0.82 = 0.7462.
- Probability of pregnancy from both: 1 − 0.7462 = 0.2538.
- Expected pregnancies with dual use: 0.2538 × 1000 ≈ 254.
- Expected pregnancies with OCP only: 0.09 × 1000 = 90.
- Reduction due to dual use: 254 − 90 = 164.
Common mistake: Adding failure rates instead of using probability of no pregnancy
Concept tested: Combined contraceptive effectiveness
Published · How this solution was prepared and checked
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