A recent survey indicated that 82% of single women aged 25 years old will be married in their lifetime. Using the binomial distribution, find the probability that two or three women in a sample of twenty will never be married.

Let X be defined as the number of women in the sample never married

$P(2\le X\le 3)=p(2)+p(3)\phantom{\rule{0ex}{0ex}}=(202)(.18)2(.82)18+(203)(.18)3(.82)17\phantom{\rule{0ex}{0ex}}=.173+.228=.401\phantom{\rule{0ex}{0ex}}$

My Question

If I recognize it effectively, the binomial distribution is a discrete chance distribution of a number of successes in a sequence of n unbiased sure/no experiments.

But choosing 2 (or 3) women from a 20-women sample is not independent experiments, because choosing the first woman will affect the probability for the coming experiments.

Why the binomial distribution was used here ?

Let X be defined as the number of women in the sample never married

$P(2\le X\le 3)=p(2)+p(3)\phantom{\rule{0ex}{0ex}}=(202)(.18)2(.82)18+(203)(.18)3(.82)17\phantom{\rule{0ex}{0ex}}=.173+.228=.401\phantom{\rule{0ex}{0ex}}$

My Question

If I recognize it effectively, the binomial distribution is a discrete chance distribution of a number of successes in a sequence of n unbiased sure/no experiments.

But choosing 2 (or 3) women from a 20-women sample is not independent experiments, because choosing the first woman will affect the probability for the coming experiments.

Why the binomial distribution was used here ?