Q:

Patient, Doctor and flu vaccination

The Department of Health encourages young children to have a flu vaccination each year.  The vaccination reduces the likelihood of getting a flu from 40% to 10%.  If 45% of the young children visiting the doctor have the vaccination, find the probability that an young child chosen at random had the vaccination, given that he/she get flu. 
Answer.  How to use here bayes'theorem for finding out answer?  I have to choose any one of the following:-
1)0.330
2)0.045
3)0.170
4)0.265
5)doubtful

A:

Let $V$ denote presence of vaccination and $F$ denote presence of flu. 
$P(V \vert F)=\frac{P(F \vert V)P(V)}{P(F \vert V)P(V)+P(F\vert \neg V)P(\neg V)}=\frac{0.1\times0.45}{0.1\times 0.45+0.4 \times0.55}$

