Mathematical Probability 1 (MATS2105)
Mathematics and Computer Science - MCS
Semester: First Semester
Level: 200
Year: 2015
UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE
CONTINUOUS EVALUATION
DEPARTMENT:MATH and CSC INSTRUCTOR: Dr. Shu F. Che
MONTH: COURSE CODE:MATS2105
YEAR: 2015 TITLE:MATHEMATICAL PROBABILITY I
DATE: TIME:
TIME ALLOWED: 2 HOURS CREDIT VALUE: 6
1. What is a probability space ? 3 pts
2. Let Ω be a non empty set, ℱ =
∅, Ω
, Ρ →[0 1] with P(Ω) = 1 — P(∅) = 1. Show that according to your
definition in question 1, (Ω, ℱ, P) is a probability space. 5pts
3. Let (Ω, ℱ, P) be a probability space and A and B be elements of 7. Prove that P(A\B) = P(A) - P(A nB).
3pts
4. Let A, B and C be events. Write down expressions for each of the following events:
(a) At least two of A, B and C occur, (t) At most two of A, B and C occur. 1 pt each
5. A communication system is to consist of m seemingly identical antennas that are to be lined up in a
linear order. The resulting system will be functional" if no two consecutive antennas are defective. Find
the probability that the resulting system is functional if it turns out that exactly n of the m antennas are
functional . 2 pts
6. A community consists of 10 men each of whom has 3 sons. If one man and two of his sons are to be chosen
as father and son of the year,
(a) how many different choices are possible? 1 pt
(b) in how many ways can these choices be made ? 1 pt
7. How many different letter arrangements can be formed using the letters PEPPEREATER-
SCOMMITTEES ? 2 pts
8. A class consists of 6 men and 4 women. An examination is given and the students are ranked according to
their performance. Assume that no two students obtained the same score.
(i) How many different rankings are possible? lpt (ii If the men are ranked among themselves and the
women among themselves, how many different rankings are possible? lpt
9. From a group of 5 men and 8 women, how many different committees consisting of 2 men and 4 women
can be formed? What if three of the women do not want to serve on the same committee? 2pts
10. A class is made of 7 boys and 8 girls. If two of the students are selected at random and asked to leave the
room,
(a) what is the probability that they are of different sexes? (6) what is the probability that they are of the
same sex? (c) what is the probability that they are both boys? 3 pts
11. An experiment consists of tossing a coin with the sides labeled H and T, and two non identical three sided
die with the sides labeled 1, 2,3 simultaneously.
(i) write down the sample space associated with this experiment. 1 pts (ii) Given that all outcomes are
equally likely find the probability that the coin lands heads, lpts (iii) Find the probability that a three is
landed by a die. 1 pts
12. In order to start playing a game of chance with a die, it is necessary that you first toss a six. (a) what is the
probability that to toss your first six at your third attempt ? 1 pt (6) what is the probability that you
require more than three tosses to get your first six? 2 pts
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