Imagine this scenario: you are the Director of a local government program that gives free mammogram screenings to low-income women. From the empirical (real-world) data your team has gathered from their patients in the past five years, you have found that the probability of a positive test result is 0.1 for women ages 40 to 49, and 0.3 for women ages 50 to 65. But after following up with more tests, it turns out that the probability of a false positive (that is, a "positive" test result when there is actuallynobreast cancer)among all positive resultsis 0.6 for ages 40-49, and 0.05 for ages 50-65.Knowing this information, how would you use probabilities to allocate this year's limited funding for your program to where it is most effective? Whatever choice you make, present the reasoning behind itusing a discussion of the probabilities (incorporating the multiplication rule and a tree diagram), along with your own judgement