This is in Statistics and Probability. Provide clear clean and neat solutions... Used digital and explain the answer

3. A researcher gathers the following data for 1000 women, of which 8 are known to have breast cancer. All 1000 women undergo the same test to determine whether or not they have breast cancer, and 77 test positive. Seven of the 8 that have breast cancer are tested positive, and 70 of those that do not have breast cancer test positive. Let A = the event that the selected woman has breast cancer, B = the event that the selected woman is tested positive. A) Give the value of each of the following probabilities: P(A) = P(A') = P(B ) A) = P(B' A) = P(B) A')= P(B'| 4') = B) Find the probability that a randomly selected woman from this group has breast cancer, given that she is tested positive. Use P(B) = P(AnB) + P(BRA') = P(B) A) . P(A) + P(B) A) . P(A') P(A| B) . P(A) and P( A B) = P(B)