IMSA Probability and Combinatorics

Question 1

A bag has 4 red and 6 blue marbles. What is the probability of picking a red marble?

Accepted Answer

2/5

Answer

P(red) = 4/(4+6) = 4/10 = 2/5.

Question 2

How many ways can you arrange 4 books on a shelf?

Accepted Answer

24

Answer

The number of arrangements of 4 items is 4! = 4 × 3 × 2 × 1 = 24.

Question 3

A coin is flipped three times. What is the probability of getting exactly 3 heads?

Accepted Answer

1/8

Answer

P(HHH) = (1/2)³ = 1/8, since each flip is independent with probability 1/2.

Question 4

A die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

1/3

Answer

Numbers greater than 4 on a standard die are 5 and 6, giving P = 2/6 = 1/3.

Question 5

How many 2-digit codes can be formed using digits 1-5 if repetition is allowed?

Accepted Answer

25

Answer

Each digit can be any of 5 values, so total codes = 5 × 5 = 25.

IMSA - Intermediate Math Skill Assesment Practice Test