Suppose that 20 of a population of registered voters are wom

Suppose that 20% of a population of registered voters are women who identify themselves as Democrats. The percent of women in the population of registered voters is 50%. A randomly selected voter in the population is a woman. What is the conditional probability this individual will identify herself as a Democrat given that we know she is a woman

Solution

Here,

P(democrat|woman) = P(democrat and woman) / P(woman)

As

P(Democrat and woman) = 0.20
P(woman) = 0.50

Then

P(democrat|woman) = 0.20/0.50 = 0.40 [answer]