Doctoral Degrees. The U.S. National Science Foundation publishes data on doctoral degrees conferred in the document Science and Engineering Doctorate Awards. The following joint probability distribution summarizes the doctoral degrees conferred in the social sciences and psychology by gender during one year. Gender Field Social science Psychology F1 F2 P(Gi)

Male 0.300 0.119 0.419 G1 Female 0.282 0.298 0.581 G2 P(Fj) 0.582 0.418 1.000

a. Find P(G1), P(F1), and P(G1 & F1).

b. Use the special multiplication rule to determine whether events G1 and F1 are independent.