Probability / Flu Vaccinations

I'm given that 70% of residents in a nursing home are given the flu vaccination, and a doctor observes that 30% of those who have the flu have already been vaccinated against it. I am trying to find the probability that a resident gets the flu, given that they have been vaccinated against it, and then also the chance they get the flu without being vaccinated.

What I set up:

P(V) = .7

P(Vc) = .3

P(V|F) = .3

and I am trying to find:

P(F|V)

P(F|Vc)

I tried using the definition of conditional probability, so that P(F|V) = P(F intersect V) / P(V), but I can't figure out what P(F intersect V) is because I only know P(V). Can anyone point me in the right direction? Thanks!