AMC 8 Probability & Counting 1 — Questions and Answers
Question 1: A bag has 3 red and 5 blue marbles. What is the probability of randomly drawing a red marble?
- 3/8 (Correct answer)
- 3/5
- 5/8
- 1/3
Correct answer: 3/8
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?
- 3
- 6 (Correct answer)
- 9
- 12
Correct answer: 6
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?
- 1/4 (Correct answer)
- 1/2
- 1/3
- 2/3
Correct answer: 1/4
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?
- 8
- 12
- 16 (Correct answer)
- 20
Correct answer: 16
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?
- 1/6
- 1/3 (Correct answer)
- 1/2
- 2/3
Correct answer: 1/3
Numbers greater than 4 are 5 and 6, so P = 2/6 = 1/3.
Question 6: From a group of 5 students, in how many ways can 2 students be chosen for a committee?
- 5
- 8
- 10 (Correct answer)
- 20
Correct answer: 10
C(5,2) = 5!/(2! × 3!) = 10.
AMC 8 Probability & Counting 1
A bag has 3 red and 5 blue marbles.
What is the probability of randomly drawing a red marble?