How would you use probabilities to allocate the limited funding of your program to where it is most effective?

Imagine this scenario: you are the Director of a local government program that gives free mammogram screenings to low-income women. The probability of a positive test result is 0.3 for women ages 40 to 49, and 0.35 for women ages 50 to 65. But the probability of a false positive (that is, a “positive” test result when no breast cancer is present) among all positive results is 0.8 for ages 40-49, and 0.2 for ages 50-65. Knowing this information, how would you use probabilities to allocate the limited funding of your program to where it is most effective? Whatever choice you make, present the reasoning behind it using a discussion of the probabilities along with your own judgement. Please respond to the prompt in roughly 300-500 words.