Lucys statistics professor asked Approximately 43 of marriag

Lucy’s statistics professor asked, “Approximately 43% of marriages in the US end in divorce within 15 years. If I take random sample of 40 couples married in June of 2014, what is the probability that half of them will be divorced by June of 2029?”. Explain how Lucy knows this is a binomial probability problem.

Solution

Prob for any random marriage end in divorce within 15 years = 0.15

n = 40

As each couple is independent, and there are only two outcomes,

X = no of couples divorced within 15 years is binomial

(0.43, 40)

the probability that half of them will be divorced by June of 2029

= P(X=20)

=0.0844