Question 1 [20 marks]
1.1 Briefly explain the following terminologies as they are applied in set theory and prol.>ability
theory.
(i) Set
[2]
(ii) Random experiment
[2]
(iii) Sample space
[2]
(iv) Event
[2]
(v) Independent events (say A and B)
[2]
1.2 Consider the events A = {l, 3}, B = {2, 5}, C = {6}, D = {3, 4} over a possibility space
S = {l, 2, 3, 4, 5, 6}.With reasons, state whether true or false
(i) Events A,B and C are pairwise mutually
[2]
(ii) {A, B, C, D} is a partition of the sample space S
[3]
(iii) 0c= {1, 2, 3, 4, 5}
[2]
(iv) .4.6..C= {1,3}
[3]
Question 2 [20 marks)
2.1 Suppose that there were 120 students in the classroom, and that they could be classified as
follows:
Gender
Male
Female
Total
Hair color
Brown
20
-
50
Not Brown
-
30
-
Total
60
-
120
Let A= "student has brown hair" and B="student is male". Find:
(i) P(A n B)
[2]
(ii) P(A u B)
[2]
(iii) P(A I B)
[3]
2.2 In a certain federal prison, it is known that 2/3 of the inmates are under 25 years of age. It
is also known that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25
years of age or older. What is the probability that a prisoner selected at random from this
prison is female and at least 25 years old?
[5].
2.3 A certain federal agency employs three consulting firms (A, B, and C) with probabilities
0.40, 0.35, and 0.25, respectively. From past experience it is known that the probability of
cost overruns for the firms are 0.05, 0.03, and 0.15, respectively. Suppose a cost overrun is
experienced by the agency.
(i) What is the probability that the consulting firm involved is company C?
[5]
(ii) ·what is the probability that the consulting firms involved are both A and C
companies?
[3]
1