(Solved): 3. There Is A Relatively Cheap DNA Test For The BRCA1 Gene Mutation (which Increases Risk Of Breast ...

3. There is a relatively cheap DNA test for the BRCA1 gene mutation (which increases risk of Breast Cancer). If a person has the BRCA1 gene mutation, there is a 60% chance they will t Cancer in their lifetime. However, there is a 12% chance they will still develop Breast Cancer even if they do not have the BRCA1 gene mutation. Approximately 0.25% of the population has the BRCA1 gene mutation. (a) What is the probability that a randomly selected member of the population will develop Breast Cancer? (0.1212) (b) Given that a randomly selected member of the population develops Breast Cancer, what is the probability they have the BRCA1 gene mutation? (0.0124) (c) Suppose that if a person has a family history of Cancer but NOT the BRCA1 gene mu- tation, there is a 30% they will develop Breast Cancer. The proportion of the population that has both of these characteristics (family history but NOT BRCA1) is 0.24. Given that a randomly selected member of the population develops Breast Cancer but does NOT have the BRCA1 gene mutation, what is the probability they have a family history of Cancer? (0.602)