Question 1 [20 marks]
1.1 Briefly explain the following terminologies as they are applied in set theory and probability
theory.
(i) Set
[2]
(ii) Size of a set
[2]
(iii) Sample space
[2]
(iv) Event
[2]
(v) Mutually exclusive events (say A and B)
[2]
1.2 Consider the sample space S = {l, 2, 3, 4, 5, 6, 7, 8, 9, 10} and the events A = {1, 2, 5, 6},
B = {3, 4, 5, 6, 7}, C = {2, 4, 6}, D = {l, 3, 6}, E = {l, 2, 5, 9}.
(i) Are A, B, C, D , and E pairwise mutually exclusive? Explain why.
[2]
Assuming that all elements are equiprobable, find:
(ii) P(S - S)
[2]
(iii) P(A u C)
[3]
(iv) P(E - D)
[3]
Question 2 [20 marks]
2.1 The issue of health coverage in Namibia is becoming critical issue in health politics. Assume
a large-scale study was undertaken to determine who is and is not covered. From this study,
the following table of joint probabilities was produced.
Age Category
25-34
35-44
45-54
55-64
Has health insurance
0.167
0.209
0.225
0.177
Does not have health insurance
0.085
0.061
0.049
0.027
If a person is selected at random,
(i) what is the probability the person is between 25 and 34 years old and has a health insur-
ance?
[l]
(ii) what is the probability the person is between 55 and 64 years old or does not have health
insurance?
[2]
(iii) If the selected person is below 55 years of age, what is the probability that he/she has
health insurance?
[4]
2.2 The proportion of people in a given community who have a certain disease is 0.005. A test
is available to diagnose the disease. If a person has the disease, the probability the test
will produce a positive signal is 0.99. If a person does not have the disease, the probability
that the test will produce a positive signal is 0.01. If a person tests positive, what is the
probability that the person actually has the disease?
[5].
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