Solving probability The question goes ,"In a random survey of $1000$ people, it is found that 7% have lung problem.Of those who have lung problems,40% are heavy smokers,50% are moderate smokers and 10% are non-smokers.For those who do not have any lung problems,10% are heavy smokers,70% are moderate smokers and 20% are non-smokers.If a person is found as a heavy smoker,what is the probability of that person having a lung problem?" I don't know how exactly to tackle this problems,any help will be appreciated

**Hint:** We want to compute $\Pr[\text{lung prob} \mid \text{heavy}]$, which is given by: $$ \frac{\Pr[\text{lung prob}]\Pr[\text{heavy} \mid \text{lung prob}]}{\Pr[\text{lung prob}]\Pr[\text{heavy} \mid \text{lung prob}] + \Pr[\text{no lung prob}]\Pr[\text{heavy} \mid \text{no lung prob}]} $$