A river splits into branches A and B to form a river island. The river bifurcation occurs downstream of the effluent discharge from a sewage treatment plant, whose efficiency is under scrutiny by the...

A river splits into branches A and B to form a river island. The river bifurcation occurs downstream of the effluent discharge from a sewage treatment plant, whose efficiency is under scrutiny by the river regulation agency. Dissolved oxygen (DO) concentrations in branches A and B are indicative of eventual pollution caused by the effluent discharge. Experts estimate the probabilities that river branches A and B have DO levels below regulatory standards are 2/5 and 3/4, respectively. They further estimate the probability of at least one of the two river branches being polluted is 4/5. (a) Determine the probability of branch A being polluted, given that branch B is polluted; (b) Determine the probability of branch B being polluted, knowing that branch A is polluted.