The following joint probability distribution summarize the doctoral degrees conferred in the social science and psychology by gender during one year. Field Social Science Psychology F1 F2 P(Gi) Gender...

 The following joint probability distribution summarize the doctoral degrees conferred in the social science and psychology by gender during one year.

                                     Field

                       Social Science                         Psychology

                        F1                                   F2                            P(Gi)

Gender

Male.           0.300                                 0.119                         0.419

G1

Female       0.282                                   0.298                         0.581

G2

P(Fj)           0.583                                   0.418                        1.000

I need

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

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