Question

Asked Jun 19, 2019

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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

Step 1

In this question, a table has given to us which shows the joint probability distribution, based on which we have to find the probabilities.

Step 2

Part 1)

P(G1) = Probability of selecting a male

In the table, there is a column named P(Gi) which shows the probability of selecting male, female. Therefore, the intersection cell of P(Gi) and Male(G1) shows the probability of selecting the male = 0.419.

**P(Gi) = 0.419**

And P(G) = 1, because which means either selecting Male or female, the sum of probability of selecting Male or female is 1, 0.419 + 0.580 = 1.

Similarly, P(F1), where F1 denotes Social Science, probability of selecting a person with doctoral degree in Soc...

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