In the general population, one woman in ten will develop breast cancer. Research has shown that 1 woman in 600 carries a mutation of the BRCA gene. Seven out of 10 women with this mutation develop breast cancer.
a) Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.
b) Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.
c) Are the events of carrying this mutation and developing breast cancer independent or dependent?