The following table presents the 100 senators of the 115th U.S. Congress on January 3, 2017, classified by political party affiliation and gender.
A senator is selected at random from this group. Compute the following probabilities.
a. The senator is a male Republican.
b. The senator is a Democrat or a female.
c. The senator is a Republican.
d. The senator is not a Republican.
e. The senator is a Democrat.
f. The senator is an Independent.
g. The senator is a Democrat or an Independent.
Let R, D, and I denote the events that the senator is a Republian, Democrat, or Independent, respectively, and let M and F denote the events that the senator is male or female, respectively.
(a) P(R ? M) = 0.47
(b) P(D
F)=P(D) + P(F) ? P(D? F)
=(0.30 + 0.16) + (0.16 + 0.05) ? 0.16
=0.51
(c) P(R)=P(R ? M) + P(R ? F)
=0.47 + 0.05
=0.52
(d) 
= 1?P(R) = 1?0.52 = 0.48
(e) P(C)=P(D? M) + P(D? F)
=0.30 + 0.16
=0.46
(f) P(I)=P(I ? M) + P(I ? F)
=0.02 + 0
=0.02
(g) P(DI) = P(D) + P(I) = 0.46 + 0.02 = 0.48
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