The practical test for driving licence consists on two indep

The practical test for driving licence consists on two independent parts A and B. to pass the practical test a candidate must pass in both parts. If a candidate fails in any one of the these parts, the candidate may take that part again.statistics show that passing % of part A and part B are 70% and 60% respectively. What is the probability that a candidate take the practical test and passes the practical test in no more than two attempts in each part.

Solution

The practical test for driving license consists of two independent parts A and B. To pass the practical test a candidate must pass in both parts. If a candidate fails in any one of the these parts, the candidate may take that part again. Statistics show that 70% of candidates pass part A and 60% pass part B.

The probability that a candidate passes the practical test in no more than two attempts of each part has to be determined.

The required probability is: (0.7 + 0.3*0.7)(0.6 + 0.4*0.6) = 0.91*0.84 = 0.7644

There is a 76.44% probability that the test is passed in no more than 2 attempts in each part.