Pharmaceutical companies advertise for the birth control pill an
annual efficacy of 99.7% in preventing pregnancy. However, under
typical use the real efficacy is only about 93%. That is, 7% 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
(b) Give your answer using the real efficacy of the pill. Please use 4 decimal places.
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