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Problem 106 Hard Difficulty

Use the information in the Table 3.19 to answer the next eight exercises. The table shows the political party affiliation of each of 67 members of the US Senate in June 2012, and when they are up for reelection.
TABLE CANNOT COPY

Suppose that a member of the US Senate is randomly selected. What is the probability that the senator is up for reelection in November 2014, knowing that this senator is a Republican?

Answer

0.35

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Video Transcript

Hi. We're answering the question that I asked about the U. S. Senators and what the probability is that the senator is up for re election in November 2014 knowing that the senator is a Republican. So, as you see on the screen, that's the probability that you're re elected that the re election in November 2014 given that they're Republican. So when we have to calculate a probability of one thing given another, remember, it's the probability of a given B, which is equal to the probability of A and B over the probability of B. So in this case, it's gonna be the probability of re electing in November 2014 given that there were Republican. So we need to calculate the probability that their elected in November 2014 and are Republican over the probability that they're Republican. And so the probability that then on, like, re elected in November 2014 and the Republican is on our chart so we can follow the reelect November 2014 over, and we find the column that has Republican above it. And there are 13 Republicans that are also re elected in November 2014 and then because it's given the probably Republican. We want to calculate the total for that Republican column if you haven't already. So that's 13 plus 24 for a total of 37 Republican senators in this survey. So we're gonna take the 13 divided by the 37 which gives us 0.35 for a final answer. Thank you.