Decision theory problem qAccording to the Spring 2009 issue

Decision theory problem

q;According to the Spring 2009 issue of the periodical Zero Population Growth, the U.S. leads the fully industrialized world in teen pregnancy rates, with 25% of U.S. females getting pregnant at least once before the age of 20. Suppose that 10 U.S. females are selected at random. Find the probability that the number who have been pregnant at least once before age 20 will be exactly three. (hint: use the binomial probability distribution)

Solution

Probability of female getting pregnant before 20 = 0.25 = p

Probability of female not getting pregnant before 20 = 1 - p = 0.75

p = success rate

q = 1 - p = failure rate

Thus, probability that 3 out of 10 got pregnant before 20

= ¹⁰C₃ p^rq^n-r

= ¹⁰C₃ (0.25)³ (0.75)⁷

=0.2502

= 25.02 % chance that exactly 3 out of 10 will have been pregnant before the age 20

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