Doctoral Degrees. The U.S. National Science Foundation publishes data on doctora
ID: 3226060 • Letter: D
Question
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 in conferred in the social sciences and psychology by gender during one year.
Field
Gender
Social Science F1
Psychology F2
P (Gi)
Male G1
0.300
0.119
0.419
Female G2
0.282
0.298
0.581
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.
Gender
Social Science F1
Psychology F2
P (Gi)
Male G1
0.300
0.119
0.419
Female G2
0.282
0.298
0.581
P (Fj)
0.582
0.418
1.000
Explanation / Answer
a) P(G1) = 0.419
P(F1) = 0.582
P(G1 and F1) = 0.3
b) P(G1) * P(F1) = 0.419 * 0.582 = 0.244
Since, P(G1 and F1) is not equal to P(G1) * P(F1) , both G1 and F1 are not independent events.
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