A class has students who are very intelligent, medium, or below average. The probabilities of failing a viva voce exam are 0.1, 0.3, and 0.5 respectively for each group. Using Bayes' rule, the probability a student who passed the exam is below average can be calculated by dividing the probability of being below average and passing by the total probability of passing.

1. P2:
In a class of students, were considered to be very intelligent, as
medium and the rest of them are below average. The probability that a very
intelligent student fails in a viva – voice examination is ; the medium
student failing has a probability ; and the corresponding probability for a
below average student is . If a student is known to have passed the
viva – voice examination, what is the probability that he is below average?
Solution:
Let us define the following events
: The student of the class is very intelligent
: The student is medium
: The student is below average
: The student passes in the viva- voice examination.
Then, we are given:
; ;
;
Required to find .
If a student is known to have passed the viva – examination, the probability that
he is below average, is given by Bayes’ rule as follows.