Math Probability and Counting Principles

Question 1

A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?

Accepted Answer

3/12

Answer

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?

Accepted Answer

1/9

Answer

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?

Accepted Answer

120

Answer

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?

Accepted Answer

35

Answer

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)?

Accepted Answer

0.7

Answer

For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.4 + 0.3 = 0.7.

Math Practice Test

Math Practice Test

Math Probability and Counting Principles