Question

2. President Donald Trump has promised to pass a bill to build a wall on the U.S. border. Polls show that 90% of registered Democrats are against this bill, while 60% of registered Republicans and 50% of registered Independents favor the bill. The distribution of party affiliation is 35% Democrat, 30% Republican, and 35% Independent.

a. What is the probability that someone picked at random does not favor the bill?

b. Suppose a randomly selected person does favor the bill. What is the probability that they are registered as a Republican?

Answer 1

a)

P(Favor)=P(Democrats)*P(Favor|Democrats)+P(Republicans)*P(Favor|Republicans)+P(Independent)*P(Favor|Independent)
	=0.35*0.1+0.3*0.6+0.35*0.5=0.39

therefore P(not favor) =1-0.39 =0.61

b)

P(Republicans|Favor)=P(Republicans)*P(Favor|Republicans)/P(Favor)=0.3*0.6/0.61 =0.4615