MATH 110 MODULE 5: PROBABILITY
AND COUNTING RULES EXAM 2026/2027
UPDATE. JUST RELEASED
1. A jar contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are
drawn without replacement, what is the probability that both are red?
A. 1/4
B. 2/9
C. 5/18
D. 25/100
Answer: B
Conceptual Explanation: The probability of the first red marble is 5/10. Since it is without
replacement, the probability of the second red marble is 4/9. (5/10) * (4/9) = 20/90 = 2/9.
2. Which of the following conditions must be met for two events A and B to be considered
mutually exclusive?
A. P(A and B) = 0
B. P(A or B) = P(A) + P(B) - P(A and B)
C. P(A and B) = P(A) * P(B)
D. P(A | B) = P(A)
,Answer: A
Conceptual Explanation: Events are mutually exclusive if they cannot occur at the same
time, meaning their intersection (A and B) is zero.
3. If the probability of an event occurring is 0.35, what are the odds against the event?
A. 7:13
B. 13:7
C. 7:20
D. 20:7
Answer: B
Conceptual Explanation: P(event) = 0.35 = 7/20. P(not event) = 0.65 = 13/20. Odds
against are P(not event) : P(event), which is 13:7.
4. How many different 4-letter permutations can be formed from the letters in the word
‘NUMBER’?
A. 360
B. 720
C. 24
D. 15
Answer: A
, Conceptual Explanation: The word ‘NUMBER’ has 6 distinct letters. The number of 4-
letter permutations is 6P4 = 6 * 5 * 4 * 3 = 360.
5. A committee of 3 people is to be formed from a group of 8. How many different
committees are possible?
A. 56
B. 336
C. 24
D. 112
Answer: A
Conceptual Explanation: Since the order does not matter in a committee, use
combinations: 8C3 = (8 * 7 * 6) / (3 * 2 * 1) = 56.
6. If P(A) = 0.6, P(B) = 0.3, and A and B are independent, what is P(A or B)?
A. 0.72
B. 0.18
C. 0.90
D. 0.42
Answer: A
Conceptual Explanation: For independent events, P(A and B) = P(A)P(B) = 0.60.3 = 0.18.
P(A or B) = P(A) + P(B) - P(A and B) = 0.6 + 0.3 - 0.18 = 0.72.
AND COUNTING RULES EXAM 2026/2027
UPDATE. JUST RELEASED
1. A jar contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are
drawn without replacement, what is the probability that both are red?
A. 1/4
B. 2/9
C. 5/18
D. 25/100
Answer: B
Conceptual Explanation: The probability of the first red marble is 5/10. Since it is without
replacement, the probability of the second red marble is 4/9. (5/10) * (4/9) = 20/90 = 2/9.
2. Which of the following conditions must be met for two events A and B to be considered
mutually exclusive?
A. P(A and B) = 0
B. P(A or B) = P(A) + P(B) - P(A and B)
C. P(A and B) = P(A) * P(B)
D. P(A | B) = P(A)
,Answer: A
Conceptual Explanation: Events are mutually exclusive if they cannot occur at the same
time, meaning their intersection (A and B) is zero.
3. If the probability of an event occurring is 0.35, what are the odds against the event?
A. 7:13
B. 13:7
C. 7:20
D. 20:7
Answer: B
Conceptual Explanation: P(event) = 0.35 = 7/20. P(not event) = 0.65 = 13/20. Odds
against are P(not event) : P(event), which is 13:7.
4. How many different 4-letter permutations can be formed from the letters in the word
‘NUMBER’?
A. 360
B. 720
C. 24
D. 15
Answer: A
, Conceptual Explanation: The word ‘NUMBER’ has 6 distinct letters. The number of 4-
letter permutations is 6P4 = 6 * 5 * 4 * 3 = 360.
5. A committee of 3 people is to be formed from a group of 8. How many different
committees are possible?
A. 56
B. 336
C. 24
D. 112
Answer: A
Conceptual Explanation: Since the order does not matter in a committee, use
combinations: 8C3 = (8 * 7 * 6) / (3 * 2 * 1) = 56.
6. If P(A) = 0.6, P(B) = 0.3, and A and B are independent, what is P(A or B)?
A. 0.72
B. 0.18
C. 0.90
D. 0.42
Answer: A
Conceptual Explanation: For independent events, P(A and B) = P(A)P(B) = 0.60.3 = 0.18.
P(A or B) = P(A) + P(B) - P(A and B) = 0.6 + 0.3 - 0.18 = 0.72.
