Fill in the following contingency table to answer this question about the curren

Question

Fill in the following contingency table to answer this question about the current US House of Representatives. Note: There is one vacancy.

a. If a representative is chosen at random, what is the probability that they will be a Republican, P(R)?

b. If a woman is chosen at random, what is the probability that she will be a Republican, P(R|W)?

c. If a representative is chosen at random, what is the probability that they will be a female independent, P(W I)?

d. If a representative is chosen at random, what is the probability that they will be a Republican woman OR an Democrat man, P[(R W) (D M)]?

Explanation / Answer

Men. Women. Total

Republican. 207 23. 240

Democrats 128. 66. 194

Independent. 0. 0. 0

Total. 335. 89. 434

A) P(R) = 240/434 = 0.553

B) P(R | W) = P(R and W) / P(W) = (23/434)/(89/434) = 23/89 = 0.2584

C) P(W and I) = 0

D) P[(R W) (D M)] = (23 + 128)/434 = 0.3479

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