Pharmaceutical companies advertise for the birth control pill an annual efficacy of 98.6% in preventing pregnancy. However, under typical use the real efficacy is only about 95%. That is, 5% of women taking the pill for a year will experience an unplanned pregnancy that year. The difference between these two rates is that the real world is not perfect: for example, a woman might get sick or forget to take the pill one day, or she might be prescribed antibiotics which interfere with hormonal metabolism. If a sexually active woman takes the pill for the four years she is in college, what is the chance that she will become pregnant at least once? (Assume that the chance of pregnancy for each year is independent).

Answer 1

To calculate the probability of getting pregnant at least once in the four years, we first calculate the probability of NOT getting pregnant each year and then multiply those probabilities together to find the probability of not getting pregnant throughout all four years. Finally, we subtract that probability from 1 to find the probability of getting pregnant at least once.

The probability of not getting pregnant in a single year is 1 - 0.05 = 0.95.

The probability of not getting pregnant all four years = 0.95 * 0.95 * 0.95 * 0.95 = 0.8145 (rounded to four decimal places).

Finally, the probability of getting pregnant at least once in the four years = 1 - 0.8145 = 0.1855, or about 18.55%.