The U.S. Senate was composed of 53 Democrats and 47 Republicans. Of the Democrats, 38 served in the military, whereas 28 of the Republicans had seen military service. If a senator selected at random had served in the military, what is the probability that he was Republican? (Note: No congresswoman had served in the military.)

Question

Quizplus · Accepted Answer

Out of the total number of senators: 
- Democrats who served in the military = 38 
- Republicans who served in the military = 28

The total number of senators who served in the military = 38 + 28 = 66

If a senator selected at random had served in the military, the probability that he was Republican can be calculated using Bayes’ theorem as follows:

P(Republican | served in military) 
= P(served in military | Republican) * P(Republican) / P(served in military)

= 28/66 * 47/100 / (66/100)

= 0.424

Therefore, the answer is B.

The US Senate Was Composed of 53 Democrats and 47 Republicans