Pharmaceutical companies advertise for the birth control pill an annual efficacy

Question

Pharmaceutical companies advertise for the birth control pill an annual efficacy of 98.7% in preventing pregnancy. However, under typical use the real efficacy is only about 94%. That is, 6% 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).

(a) Give your answer using the theoretical efficacy of the pill. Please use 4 decimal places.


(b) Give your answer using the real efficacy of the pill. Please use 4 decimal places.

Explanation / Answer

a)

theoretical efficacy

probability of getting pregnent
q=0.987
here n=4
P(atleast once)=1-P(0)
=1-(4C0 p^0*q^4)
= 1-(0.987)^4
=0.050994

b)

real world
probability of getting pregnent =p = 0.06
q=0.94
here n=4
P(atleast once)=1-P(0)
=1-(4C0 p^0*q^4)
= 1-(0.96)^4
=0.15065

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