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Problem 105 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. Given that the randomly selected senator is up for reelection in November 2016, what is the probability that this senator is a Democrat?

Answer

0.2941

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Video Transcript

Hi. So we're answering the question that I asked about the randomly selected senator. We know that's a randomly selected senator. We want the probability that, um, it's a Democrat, given that we know it's a randomly selected senator from the November 2016 re election, which is what I have written here on the screen. So if you remember to calculate a given kind of probability, for example, if we have the probability of a given B, that's equal to the probability of A and B together over the probability of B. So we're gonna do the same kind of thing here to answer this question and put it in terms of the question itself. So the probability that it's a Democrat, given that they're re electing in November 2016. So that would be equal to the probability that it's a Democrat and the November 2016 election over the probability of all the senators in the November 2016 election. So we're gonna look at our table and the 1st 1 the numbers given to us. We just need to look in the Democrat column and go down to the road. This is re elect November 2016 and you'll see that there's 10 senators in that column, and then we're gonna use the road that says November 2016 reelection. We would need to add those up if you haven't already done that. So 10 plus 24 which is 34 and then we use our calculator to divide that and we end up with zero point 29 for one, and that's all there is having a.