The registrar of Computronics Institute has compiled the following statistics on the progress of the school's students in their 2-yr computer programming course leading to an associate degree: Of beginning students in a particular year, 80% successfully complete their first year of study and move on to the second year, whereas 20% drop out of the program; of second-year students in a particular year, 85% go on to graduate at the end of the year, whereas 15% drop out of the program. Determine the probability that a beginning student enrolled in the program will complete the course successfully.

A) 0.9
B) 0.75
C) 0.68
D) 0.51

Question

The registrar of Computronics Institute has compiled the following statistics on the progress of the school's students in their 2-yr computer programming course leading to an associate degree: Of beginning students in a particular year, 80% successfully complete their first year of study and move on to the second year, whereas 20% drop out of the program; of second-year students in a particular year, 85% go on to graduate at the end of the year, whereas 15% drop out of the program. Determine the probability that a beginning student enrolled in the program will complete the course successfully.
​
A) 0.9
B) 0.75
C) 0.68
D) 0.51

Quizplus · Accepted Answer

We can use the multiplication rule of probability to calculate the probability that a beginning student enrolled in the program will complete the course successfully:

P(successful completion) = P(completing 1st year successfully) x P(graduating in 2nd year | completed 1st year successfully)

P(completing 1st year successfully) = 0.8 (given)
P(graduating in 2nd year | completed 1st year successfully) = 0.85 (given)

Therefore, 
P(successful completion) = 0.8 x 0.85 = 0.68

So, the probability that a beginning student enrolled in the program will complete the course successfully is 0.68. Hence, the best choice is C.

The Registrar of Computronics Institute Has Compiled the Following Statistics