Question

question 1. In STAT4800-W02, there are two term tests and, it is believed that the term test 2 is harder than
the term test 1. You believe the probability you pass the term test 1 is 70%. If you pass the term
test 1, the probability you also pass the term test 2 will be 80%, and if you fail the term test 1,
the probability you pass the term test 2 will be 20%. Let ? be the number of term tests you pass.
a) Find the probability model for ?.
b) Find and interpret the expected number of tests you pass. What is your recommendation to
your friend, about this instructor, who is planning to take the STAT4800 in next semester?
(1.5 marks)

Answer 1

Q1) The probability model for X here is obtained as:
P(X = 0) = P(Term 1 fail)*P(Term 2 fail given that Term 1 was failure)
P(X = 0) = (1 - 0.7)*(1 - 0.2) = 0.3*0.8 = 0.24

P(X = 2) = P(Term 1 pass)*P(Term 2 pass given that Term 1 was passed)
P(X = 2) = 0.7*0.8 = 0.56

Therefore, P(X = 1) = 1 - P(X = 0) - P(X = 2) = 1 - 0.24 - 0.56 = 0.2

Therefore the probability model here is given as:
P(X = 0) = 0.24,
P(X = 1) = 0.2,
P(X = 2) = 0.56

b) The expected number of tests passed is computed here as:
E(X) = 0*0.24 + 1*0.2 + 2*0.56 = 1.32

Therefore 1.32 is the expected number of tests passed here. As the expected value here is 1.32, the interpretation os this is that in long term, the average number of tests passed by any person is given as 1.32 tests.

Given that there is a high probability of failing tests here, and only 0.56 as the probability of passing both tests, therefore we would not recommend our friend to take the course here.