Question: BLUECREST UNIVERSITY
Monrovia, Liberia
SCHOOL OF GRADUATE STUDIES
SPRING 2026
QUESTION PAPER
Name of the Program: MSc IT
Name of the Subject: Advanced Mathematics for
IT
Subject Code: MIT556
Semester: 1
Date of the Exam: 14 August, 2026
Exam-type: Mid-term (Resit)
Student Name:
Duration of the Exam: 1 Hour 30 Minutes
Total Marks: 30
Section A [Short Answer]
Answer any 5 questions from section A. Each question carries 2-marks. (5x2 = 10 Marks)
1. Define biconditional proposition in logic with example.
2. Express the statement “If it rains, then the roads are wet” in symbolic form.
3. Give the symbolic form of the statement “All students who study regularly pass the
examination.”
4. A box contains 8 red balls, 5 blue balls, and 3 green balls. Two balls are drawn at
random without replacement. Find the probability that both are red.
5. What is the probability that a non-leap year selected at random will contain 53
Sundays?
Section B [Long Answers]
Answer any 4 questions from section B. Each question carries 5-marks. (4 * 5 = 20 Marks)
1. Show that QV(P∧¬Q)V(¬PV¬Q) is a tautology.
2. Show that (x) (P(x) → Q(x))∧(Q(x) → R(x)) (x)(P(x) → R(x)).
3. Obtain the PDNF(Principal Disjunctive Normal Form) of (p ∧ q) v (¬p ∧ r) v (q ∧ r).
4. A bolt is manufactured by 3 machines A, B and C. A turns out twice as many items as
B, and machines B and C produce equal number of items. 2% of bolts produced by A
and B are defective and 4% of bolts produced by C are defective. All bolts are put into
1 stock pile and is chosen from this pile. What is the probability that it is defective?
5. A random variable X has the following probability distribution.
X -2 -1 0 1 2 3
P(X) 0.1 K 0.2 2k 0.3 3k
(a)Find K, (b) Evaluate P(X < 2) and P(-2 < X < 2) and (c) find the cdf of X
6. The probability that Azher, who always walks to work, arrives late on any day is 0.11.
Calculate the probability that, during a period of 20 working days, he is late on (i)
exactly 4 days; (ii) More than 2 days; and (iii) none of the day.
***All the Best***
1. **Problem:** Find the probability that both balls drawn without replacement from a box containing 8 red, 5 blue, and 3 green balls are red.
2. **Formula:** Probability of both events happening without replacement is given by
$$P = \frac{\text{number of favorable outcomes}}{\text{total outcomes}} \times \frac{\text{number of favorable outcomes after first draw}}{\text{total outcomes after first draw}}$$
3. **Step 1:** Total number of balls = $8 + 5 + 3 = 16$
4. **Step 2:** Probability that the first ball drawn is red:
$$P_1 = \frac{8}{16} = \frac{1}{2}$$
5. **Step 3:** After drawing one red ball, remaining red balls = $8 - 1 = 7$, total balls left = $16 - 1 = 15$
6. **Step 4:** Probability that the second ball drawn is red:
$$P_2 = \frac{7}{15}$$
7. **Step 5:** Probability both balls are red:
$$P = P_1 \times P_2 = \frac{1}{2} \times \frac{7}{15} = \frac{7}{30}$$
8. **Answer:** The probability that both balls drawn are red is $$\boxed{\frac{7}{30}}$$.