In a small town there are $5600$ people, who are older than $60$ years. Of these, $3200$ were vaccinated against flu last winter. Of those over $60$, $1800$ had the flu. Of those not vaccinated over $60$, $950$ remained flu-free. 

With what probability 

a) Got a vaccinated person the flu. 

b) Was a flu patient vaccinated. 

c) Did a non-vaccinated person leave flu-free. 

d) has a healthy person not been vaccinated. 

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Here we need the conditional probability, right? 

I have done the following: 

Let V the event that a perosn got vaccinated and F that a person is a flu-patient. 

Do we have to calculate the following probabilities? 

a) $P(F\mid V)$ 

b) $P(V\mid F)$ 

c) $P(\overline{F}\mid \overline{V})$ 

d) $P(\overline{V}\mid \overline{F})$ 

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EDIT1: 

So we have that a) $P(F\mid V)=\frac{P(F\cap V)}{P(V)}$ 

b) $P(V\mid F)=\frac{P(V\cap F)}{P(F)}$ 

c) $P(\overline{F}\mid \overline{V})=\frac{P(\overline{F}\cap \overline{V})}{P(\overline{V})}$ 

d) $P(\overline{V}\mid \overline{F})=\frac{P(\overline{V}\cap\overline{F})}{P(\overline{F})}$ 
or not? 

Do we have that $P(F)=\frac{1800}{5600}$, $P(V)=\frac{3200}{5600}$, $P(\overline{V}\cap\overline{F})=\frac{950}{5600}$ ? 

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EDIT2: 

Does it hold that \begin{align\*}P(F\cap V)&=1-P(\overline{F}\cup \overline{V})\\ & =1-\left (P(\overline{F})+P(\overline{V})-P(\overline{F}\cap \overline{V})\right ) \\ & =1-\left (1-\frac{1800}{5600}+1-\frac{3200}{5600}-\frac{950}{5600}\right )\end{align\*} ?