A card repair is either on time or late and either satisfact

A card repair is either on time or late and either satisfactory or unsatisfactory.If a repair is made on time, then there is a probability of 0.75 that it is satisfactory. If the repair is late, there is a probability of 0.1 that it is unsatisfactory.There is a probability of 0.6 that a repair will be made on time. If a repair satisfactory,what is the probability that it was made on time?

Solution

Using Bayes’ theorem, find if repair satisfactory,then the probability that it was made on time

0.6*0.75/(0.6*0.75+0.94*0.1)

=0.45/0.544=0.827