In a big factory, 3% of the workers are alcoholics. 65% of the alcoholic workers miss a day of work and 10% of the non-alcoholic workers also miss a day of work. A doctor justifies the absence of 5% of the alcoholic workers and 25% of the non-alcoholic workers.

a) What is the probability that a worker who is absent is an alcoholic?

b) What is the percentage of the workers who can justify their absence?

c) A worker missed a day of work and justified his absence, what is the probability of him being an alcoholic?