Women with mutations in their BRCA1 or BCRA2 genes (“carriers”) represent about 0.5% of the U.S. population (Malone et al. 2006). Women who are carriers have an 80% chance of developing breast cancer in their lifetimes (Schubert 1997). Those with normal versions of these genes have a 12% chance of developing breast cancer in their lifetime.

a. What is the probability that a randomly sampled woman from the U.S. population is a carrier of either BRCA1 or BRCA2?

b. If 10 women are sampled from the U.S. population, what is the probability that none are carriers?

c. If 20 women are sampled from the U.S. population, what is the probability that at least one is a carrier?

d. What is the probability that a randomly sampled woman from the U.S. population both is a carrier of a mutant gene and develops breast cancer in her lifetime?

e. What is the probability that a woman from the U.S. population develops breast cancer in her lifetime?

f. What is the probability that a randomly chosen U.S. woman who develops breast cancer in her lifetime is a carrier?