This is in Statistics and Probability. Provide clean and clear clean and neat solutions. Minimize erasures and provide a clear picture of the solutions thank you and Godbless.

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' | 4) = 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(AB) + P(BA') = P(BOA) + P(BAM') = P(B| A) . P(A) + P(B| A') . P(A') P(A| B) . P(A) and P(A| B) = P(B)