AMC 8 Probability & Counting 2 — Questions and Answers
Question 1: A spinner has 4 equal sections numbered 1 through 4. What is the probability of landing on a prime number?
- 1/4
- 1/2 (Correct answer)
- 3/4
- 1/3
Correct answer: 1/2
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?
- 1/6 (Correct answer)
- 1/9
- 5/36
- 7/36
Correct answer: 1/6
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?
- 8
- 12
- 16
- 24 (Correct answer)
Correct answer: 24
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)?
- 1/13
- 3/13 (Correct answer)
- 3/52
- 1/4
Correct answer: 3/13
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?
- 60 (Correct answer)
- 80
- 120
- 240
Correct answer: 60
C(5,3) × C(4,2) = 10 × 6 = 60.
Question 6: How many 3-digit even numbers can be formed from {2, 4, 5, 6} with no repetition?
- 12
- 18 (Correct answer)
- 24
- 30
Correct answer: 18
Choose an even units digit (3 options: 2, 4, 6), then arrange the remaining 3 digits in the first two positions (3 × 2 = 6 ways): 3 × 6 = 18.
AMC 8 Probability & Counting 2
A spinner has 4 equal sections numbered 1 through 4.
What is the probability of landing on a prime number?