Question

Suppose that in an election voter preference is sharply divided along gender lines. 40% of women will vote for candidate A, the rest will vote for Candidate B; 70% of men will vote for Candidate A, the rest for Candidate B. Which of the following represents the lowest percentage of voters that must be women on election day, in order that Candidate B wins the election?

Answer 1

Solution: Let W be women voters and M be men voters.

40% of women will vote for candidate A=(40/100)W=0.4W

70% of men will vote for Candidate A=(70/100)M=0.7M

So total votes for candidate A=0.4W+0.7M

Total votes for candidate B=W+M-(0.4W+0.7M)=0.6W+0.3M

So, from the question we can say(in order that Candidate B wins the election),

0.6W+0.3M>0.4W+0.7M

=0.2W>0.4M

=W>2M

The lowest percentage of voters that must be women on election day, in order that Candidate B wins the election=100*2M/(M+2M)...................we know total=M+W

=100*2M/3M=66.67%

Therefore, 66.67% of voters must be women on the election day for candidate B to win.