suppose candidate A receives 54% of the entire vote, but only 48% of the female vote. A voter is selected at random for an interview. What is the probability that the voter is a woman who voted for candidate A?

You can write a formula involving the population of voters.

\(\displaystyle P=\frac{0.48W}{M+W}=\frac{0.48(0.54)W}{M_A+W_A}\)

where the subscript "A" indicates those who voted for Candidate A.

\(\displaystyle \frac{M_A+W_A}{M+W}=0.54\)

\(\displaystyle \frac{W_A}{W}=0.48\)

\(\displaystyle \frac{0.48W}{W+M}=0.48W\frac{0.54}{M_A+W_A}

\)

Different populations of men and women give different results..

For instance, if there were 100 men and 100 women

\(\displaystyle \frac{48}{100}+\frac{M_A}{100}=\frac{48+M_A}{200}=\frac{54}{100}=\frac{108}{200}\)

then \(\displaystyle M_A=60\)

but

\(\displaystyle \frac{0.48W}{W+M}=\frac{48}{200}=P\)

If we change the number of men, the probability will change.

If we change the number of women, the probability will change.