Math Probability and Counting Principles — Questions and Answers
Question 1: A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?
- 1/3
- 1/4
- 3/12 (Correct answer)
- 3/7
Correct answer: 3/12
Total marbles = 4+3+5 = 12. P(blue) = 3/12 = 1/4. Note that 3/12 simplifies to 1/4, and answer choice C (3/12) equals answer choice B (1/4); the unreduced form 3/12 is the direct calculation.
Question 2: Two fair six-sided dice are rolled. What is the probability that both show a number greater than 4?
- 1/9 (Correct answer)
- 1/6
- 1/3
- 2/6
Correct answer: 1/9
Numbers greater than 4 on one die: {5, 6} → probability = 2/6 = 1/3. For two independent dice: (1/3) × (1/3) = 1/9.
Question 3: In how many ways can 5 students be arranged in a line?
- 120 (Correct answer)
- 25
- 20
- 60
Correct answer: 120
This is a permutation of 5 items: 5! = 5×4×3×2×1 = 120.
Question 4: A committee of 3 is chosen from 7 people. How many different committees are possible?
- 35 (Correct answer)
- 210
- 21
- 42
Correct answer: 35
C(7,3) = 7!/(3!×4!) = (7×6×5)/(3×2×1) = 210/6 = 35.
Question 5: If P(A) = 0.4 and P(B) = 0.3 and A and B are mutually exclusive, what is P(A or B)?
- 0.7 (Correct answer)
- 0.12
- 0.58
- 1.0
Correct answer: 0.7
For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.4 + 0.3 = 0.7.
Question 6: A card is drawn from a standard 52-card deck. What is the probability that it is a king OR a heart?
- 4/13
- 16/52 (Correct answer)
- 17/52
- 1/4
Correct answer: 16/52
P(king) = 4/52, P(heart) = 13/52, P(king of hearts) = 1/52. P(king or heart) = 4/52 + 13/52 − 1/52 = 16/52 = 4/13.
Math Probability and Counting Principles
A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles.
What is the probability of drawing a blue marble?