IMSA Probability and Combinatorics 1 ā Questions and Answers
Question 1: A bag has 4 red and 6 blue marbles. What is the probability of picking a red marble?
- 2/5 (Correct answer)
- 4/6
- 3/5
- 1/4
Correct answer: 2/5
P(red) = 4/(4+6) = 4/10 = 2/5.
Question 2: How many ways can you arrange 4 books on a shelf?
- 24 (Correct answer)
- 12
- 16
- 8
Correct answer: 24
The number of arrangements of 4 items is 4! = 4 Ć 3 Ć 2 Ć 1 = 24.
Question 3: A coin is flipped three times. What is the probability of getting exactly 3 heads?
- 1/8 (Correct answer)
- 1/2
- 1/4
- 3/8
Correct answer: 1/8
P(HHH) = (1/2)Ā³ = 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?
- 1/3 (Correct answer)
- 1/2
- 2/3
- 1/6
Correct answer: 1/3
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?
- 25 (Correct answer)
- 10
- 20
- 15
Correct answer: 25
Each digit can be any of 5 values, so total codes = 5 Ć 5 = 25.
Question 6: What is the probability of drawing a queen from a standard 52-card deck?
- 1/13 (Correct answer)
- 4/52
- 1/4
- 1/52
Correct answer: 1/13
There are 4 queens in 52 cards, so P = 4/52 = 1/13.
IMSA Probability and Combinatorics 1
A bag has 4 red and 6 blue marbles.
What is the probability of picking a red marble?