Use the following data for the 100 Senators from the 112th Congress of the Unite

Question

Use the following data for the 100 Senators from the 112th Congress of the United States.

            Republican    Democrat     Independent

Male     42                        39               2

Female   5                         12               0

If one Senator is randomly selected, find the probability of

(a) Getting a non-Republican:

(b) Getting a male or a Republican.

(c) Getting a Democrat given that this Senator is a female. Ie. Find P(Democrat/Female).

(d) Getting a female given that this Senator is a Democrat. Ie. Find P(Female/Democrat).

Explanation / Answer

a) P(non-Republican) = (100-(42+5))/100 = 0.53

b) P(male or a Republican) = (42+5+39+2)/100 = 0.88

c) P(Democrat | Female) = P(Democrat and female)/P(Female)

= 12/(12+5) = 0.7059

d) P(Female | Democrat) = P(Democrat and female)/P(Democrat)

= 12/(39+12) = 0.2353

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