Probability question

Question

40.7% of voters are Democrats in a town, and 59.3% are Republican.  In the last election, 33.9% Democrats voted, and 38.2% Republicans voted.

 

a) If a Democrat was randomly selected, what is the probability that they voted in last election?

 

b) If a citizen who did not vote in last election was randomly selected, what is probability they are a Republican?

Answer 1

a) Given that the person is a Democrat, there's a 0.339 probability he or she voted, since 33.9% of Democrats voted.

 

b) 66.1% of Democrats didn't vote and 61.8% of Republicans didn't vote. That means that 0.661(40.7) = 26.94% of the citizens are non-voting Democrats, and 0.618(59.3) = 36.65% of the citizens are non-voting Republicans. Given that the citizen selected did not vote, he or she is one of the 26.94 + 36.65 = 63.59% who didn't vote. The probability he or she is a Republican is 36.65/63.59 = 0.576.