Question #1: Create an scenario from your own experiences that can be used to model a probability problem with related events, where there is dependency presented between the events

example

A model response might look like this: In a certain region in the country, 12% of women are diagnosed with Breast Cancer. A mammogram at the region's hospital correctly diagnoses a woman with Breast Cancer about 85% of the time. This mammography produces a false positive about 5% of the time. What is the probability that a woman that had a negative mammogram has Breast Cancer?

Question #2: Draw a Tree Diagram to show the relationship between all of your presented events. Label each part of the tree using the identified events and the corresponding probabilities. Note you should include the events and the corresponding probabilities. In all, there should be 10 entries.

example : model response might look like

o A model response might look like this: P(B n P) = (0.12)*(0.85) P(P | B) = 0.85 P(PC | B) = 0.15 P(B) = 0.12 P(B n Pc) = (0.12)*(0.15) P(B' n P) = (0. 88)*(0.05) P(P | BC) = 0.05 P( BC ) = 0.88 P(PC | BC) = 0.95 P(BC n Pc ) = (0.88)*(0.95)o A model response might look like this: Question: What is the probability that a woman receiving a positive mammogram result has Breast Cancer? P(B n P) (0.12)(0.85) Solution: P(B| P) = P(P) (0.12)(0.85) + (0.88)(0.05)