The registrar of a law school has compiled the following statistics on the progress of the school's students working toward the LLB degree: Of the first-year students in a particular year, 88% successfully complete their course of studies and move on to the second year, whereas 12% drop out of the program; of the second-year students in a particular year, 92% go on to the third year, whereas 8% drop out of the program; of the third-year students in a particular year, 95% go on to graduate at the end of the year, whereas 5% drop out of the program. Determine the probability that a beginning law student enrolled in the program will go on to graduate.

Question

Quizplus · Accepted Answer

To find the probability that a beginning law student enrolled in the program will go on to graduate, we need to multiply the probabilities of successfully completing each year.
Probability of successfully completing first year = 88% = 0.88
Probability of successfully completing second year given successful completion of first year = 92% = 0.92
Probability of successfully completing third year given successful completion of first and second year = 95% = 0.95
Therefore, 
Probability of successfully completing all 3 years = 0.88 x 0.92 x 0.95 ≈ 0.7705
So, the probability that a beginning law student enrolled in the program will go on to graduate (i.e., successfully complete all 3 years) is approximately 0.7705 or 77.05%. The best choice is C.

The Registrar of a Law School Has Compiled the Following