Question

The population of registered voters contains 45% republicans and 55% democrats. If 25% of republicans and 75% of democrats favor an issue, and a person who is chosen at random favors the issue, what is the probability that she
was a democrat?

Answer 1

This is what i have come up with so far.
P(republican) = .45
P(democrat) = .55
P(republican and favors) = .25*.45
P(democrat and favors) = .75 *.55
P(favor) = P(republican AND favors) + P (democrat AND favors)

therefore

P(democrat given that favors) = P(democrat and favors)/ (Pfavors)

Answer 2

Hm, well this is what I came up with. Still thinking about it.

45*4 republicans and 55*4 democrats, let
If 25% of republicans favor an issue means=45
and 75% of democrats favor an issue means = 165
total who favours = 210
P of her to be democrat= 165/210
.785

Answer 3

No wait

Answer 4

yeah, I got .786 too. I was confused if the question was asking about P(democrat given that she favors the bill) or something like P(democrat and favors), but we are given that in the problem statement.

Answer 5

I'm pretty sure it's ~.785

Answer 6

Would be nice to get a second opinion though

Answer 7

I get P(democrat) = 0.7857

Answer 8

same here. i just rounded up