In a population of 800 women, 500 use combined oral contraceptive pills (typical‑use failure rate 9 % per year) and 300 use male condoms (typical‑use failure rate 18 % per year). All women use only one of these methods. (a) Calculate the expected number of unintended pregnancies in one year. (b) Calculate the expected number of pregnancies if all 800 women used only combined oral contraceptive pills. (c) How many pregnancies could have been avoided if all women had used only the pills?
Answer
99 pregnancies in one year; 72 if all used OCPs; 27 avoided
The correct answer is 99 pregnancies in one year; 72 if all used OCPs; 27 avoided — Pregnancies avoided by switching all to OCPs = 99 – 72 = 27
Step-by-step solution
- For OCP users: 0.09 × 500 = 45 pregnancies
- For condom users: 0.18 × 300 = 54 pregnancies
- Total expected pregnancies in one year = 45 + 54 = 99
- If all 800 used OCPs: 0.09 × 800 = 72 pregnancies
- Pregnancies avoided by switching all to OCPs = 99 – 72 = 27
Common mistake: Misapplying percentages as decimal fractions
Concept tested: Effectiveness comparison of contraceptive methods
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