And a male candidate can win among female voters when running against a woman.
She did not come along just for company, but to win over female voters.
But in both cases, the candidates made no special efforts to win over female voters until recently.
In both states the support of undecided and independent female voters could hold the key to victory.
Polls show the Democrats losing support among female voters this year.
How is that stance likely to be received by female voters?
They show, for instance, whether there is a gender gap between male and female voters.
"It will do nothing but help them with female voters," an adviser said.
Ms. Johnson said that she was also likely to do well among minority and female voters.
This was the first time in eight elections that there has been as wide a division between male and female voters.