AMC 8 Probability & Counting 2

Question 1

A spinner has 4 equal sections numbered 1 through 4. What is the probability of landing on a prime number?

Accepted Answer

1/2

Answer

The primes among 1–4 are 2 and 3, so P(prime) = 2/4 = 1/2.

Question 2

Two fair dice are rolled. What is the probability that their sum is 7?

Accepted Answer

1/6

Answer

There are 6 pairs that sum to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 equally likely outcomes.

Question 3

In how many ways can 4 books be arranged on a shelf?

Accepted Answer

24

Answer

4 distinct books can be arranged in 4! = 4 × 3 × 2 × 1 = 24 ways.

Question 4

A card is drawn from a standard 52-card deck. What is the probability it is a face card (J, Q, or K)?

Accepted Answer

3/13

Answer

There are 12 face cards (4 Jacks + 4 Queens + 4 Kings), so P = 12/52 = 3/13.

Question 5

There are 5 boys and 4 girls. In how many ways can a team of 3 boys and 2 girls be selected?

Accepted Answer

60

Answer

C(5,3) × C(4,2) = 10 × 6 = 60.

AMC 8 - American Mathematics Competition 8 Practice Test