Question 1 [25 marks]
1.1
Assume that { Bi,B2 , ••• ,Bk}is a partition of S such that P(B;)> 0, for i = I, 2,..., k.
k
Provethatforanyevent A in the samples, P(A)=IP(AIB;)P(B;)
[SJ
i=l
1.2
Let X be a binomial random with a probability mass function given by
f(:) f(x) = pkqn-x,for x = 0,1, ..., n
l
0, elsewhere
Show that E(X) = np.
[10]
1.3
Dr.Richmond, a psychologist, is studying the daytime television viewing habits of college
students. She believes 45 percent of college students watch soap operas during the
afternoon. To further investigate, she selects a sample of 10.
1.3.1
1.3.2
1.3.3
Write down a probability distribution for the number of students in the sample who
watch soap operas.
[3]
Find the mean and variance of this distribution.
[4]
What is the probability of finding exactly four watch soap operas?
[3]
Question 2[30 marks]
2.1 Consider the experiment of tossing a fair coin three times.
2.1.1 Develop a tree diagram for the experiment.
[2]
2.1.2 List the experimental outcomes.
[8]
2.1.3 What is the probability for each experimental outcome?
[1]
2.2. A committee of 5 persons is to be formed from 6 men and 4 women. In how many
ways can this be done when:
2.2.1 at least 2 women are included?
[4]
2.2.2 at most 2 women are included?
[4)
1