AMC 8 Probability & Counting

Question 1

A bag has 3 red and 5 blue marbles. What is the probability of randomly drawing a red marble?

Accepted Answer

3/8

Answer

There are 3 red marbles out of 8 total, so P(red) = 3/8.

Question 2

How many ways can you arrange the letters in the word CAT?

Accepted Answer

6

Answer

Three distinct letters can be arranged in 3! = 3 × 2 × 1 = 6 different orders.

Question 3

A fair coin is tossed twice. What is the probability of getting two heads?

Accepted Answer

1/4

Answer

P(HH) = (1/2) × (1/2) = 1/4.

Question 4

How many 2-digit numbers can be formed using digits 1, 3, 5, 7 if repetition is allowed?

Accepted Answer

16

Answer

Each of the two digit positions has 4 choices, so there are 4 × 4 = 16 two-digit numbers.

Question 5

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

Accepted Answer

1/3

Answer

Numbers greater than 4 are 5 and 6, so P = 2/6 = 1/3.

AMC 8 - American Mathematics Competition 8 Practice Test