I think you basically have it right. The facts are that someone visited both sites and their gender presumably did not change in between visits. Thus, the question is how likely is it that a woman visits both sites. To find this you use the probability that it was a woman visiting both sites relative to the probability that it was a man visiting both sites



pW = (pWD * pWO)/ (pWD * pWO + pMD * pMO)

= (.75 * .4) /(.75 * .4 + .25 * .6)

=.67 (what mcatdog said)


where:
p is probability
W is woman
M is man
D is dillard's
O is the other website

conversely,

pM = (pMD * pMO) / (pMD * pMO + pWD * pWO)
= (.25 * .6 ) / (.25 * .6 + .75 * .4)
= .33

since pM and pW are mutually exclusive, they should add up to 1 (and they do: .67 = .33 = 1)