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Problem 104 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

What is the probability that a randomly selected senator is a Republican or is up for reelection in November 2014?

Answer

0.85

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Video Transcript

Hi, We're looking at question 104 That asked, What is the probability that a randomly selected senator is a Republican or is up for re election in November 2014? So for this one, because it's a or question, we want to be careful about double counting. And so we need to find the probability that they're Republican and the probability that they're Republican is going to be looking in the Republican column. And that would be 13 plus the 24. And that would be out of the 67 total centers. So that would be 37 out of the 67 senators. And then we also need to find the probability that there re elected in November of 2014 and for the re elected in November. We're gonna add that row, which is 20 plus 13 all over our total, which is 67. So there's 33 senators on the 67 that were re elected in 2014. But notice we've got this 13 in here twice, and those are the same 13 senators, so we don't want to count them twice. So what we're gonna do is we're gonna take our probability of Republicans, which is 37 out of 67 plus our probability of being re elected in November of 2014 which is 33 out of 67. And then we're gonna subtract though that repeats we're going to subtract the 13 on a 67. Since we have a common denominator weaken, just attract those and are well, add the 37 the 33 then subtracted 13. That's attracted all of it and do 57 over 67 then when you divide that, you get 670.8 guys, they