Using a survey on smoking status of parents, it was established that 35% of all parents

Question

Using a survey on smoking status of parents, it was established that 35% of all parents are nonsmoking parents of which 7.8% had children with pneumonia, one parent smoking percentage is 25% of which 11.4% had children with pneumonia, and both parent smoking percentage is 40% of which 17.6% had children with pneumonia. What is the probability that a randomly selected newborn will have What is the probability that a randomly selected newborn will have pneumonia?

Answer 1

The problem uses Bayes' Theorem. Let $$P(N) :probability\ of\ getting\ a\ children\ with\ pneumonia\\P(P) : probability \ that\ one \ parent\ is\ smoking\\P(nP): probability\ that\ no\ parent\ is\ smoking \\P(PP):probability\ that\ both\ parents\ are\ smoking$$

So, $$P(N) = P(N|P)*P(P) +P(N|nP)*P(nP) + P(N|PP)*P(PP)\\=.35*.078+ .25*.114+.40*.176\\= 0.1262$$