In the Democratic primary in New York, Hillary Clinton won 57.9% of the vote, an
ID: 3156076 • Letter: I
Question
In the Democratic primary in New York, Hillary Clinton won 57.9% of the vote, and Bemie Sanders won 42% of the vote. 65.6% of New York democrats support a ban on fracking in the state, while only 34.3% oppose a ban. If exit polls showed that 54.2% of Sanders' voters support the fracking ban, and 45.8% oppose it then......what are the odds that someone voted for Sanders given that we know they supported the fracking ban?...what are the odds that someone voted for Sanders given that we know they opposed the fracking ban?Explanation / Answer
a) Using conditional probability theorem or Bayes' Theorem
P( voted for sander | supported ban) = P(supoorted ban | voted for sander)*P(voted for sander) / (P(supoorted ban | voted for sander)*P(voted for sander) + P(opposed ban | voted for sander)*P(voted for sander))
P(supoorted ban | voted for Sanders) = 0.42*0.542 = 0.2276
P(voted for Sanders) = 0.42
P(opposed ban | voted for Sanders) = 0.42*0.458 = 0.1923
P( voted for sander | supported ban) = (0.2276*0.42) / (0.2276*0.42 + 0.1923*0.42)
= 0.542
(b)
Using conditional probability theorem or Bayes' Theorem
P( voted for sander | opposed ban) = P(opposed ban | voted for sander)*P(voted for sander) / (P(supoorted ban | voted for sander)*P(voted for sander) + P(opposed ban | voted for sander)*P(voted for sander))
P(supoorted ban | voted for Sanders) = 0.42*0.542 = 0.2276
P(voted for Sanders) = 0.42
P(opposed ban | voted for Sanders) = 0.42*0.458 = 0.1923
P( voted for sander | supported ban) = (0.1923*0.42) / (0.2276*0.42 + 0.1923*0.42)
= 0.4579