2. Suppose that 1% of the women in a certain population have breast cancer and that each of these women undergoes a mammogram to test for breast cancer. According to one study, the
probability that a woman without breast cancer gets a positive test result is 0.121. The
probability that a woman with breast cancer gets a negative result is 0.0015. Select one woman
from this population at random.
(a) Express the provided information using probability notation.
(b) Display the provided information using a tree diagram. Then calculate the probabilities of
each of the four possible outcomes.
(c) Calculate the probability that a randomly selected woman from this population tests
positive.
(d) Given that the test result is positive, what is the probability that the woman actually has
breast cancer?