Let's solve each probability question step by step based on the information provided. A
fair die has six faces: numbered 1 through 6.
We'll use the formula for probability:
> Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Since a fair die has 6 sides, the total number of possible outcomes is
6.
---
1. What is the probability of rolling a 3?
- Favorable outcome: only one face shows a 3.
- So, number of favorable outcomes = 1
> $$
> \text{Probability} = \frac{1}{6}
> $$
✔ Answer: $ \frac{1}{6} $
---
2. What is the probability of rolling more than 4?
Numbers greater than 4 on a die:
5 and 6
- Favorable outcomes: 5, 6 → 2 outcomes
> $$
> \text{Probability} = \frac{2}{6} = \frac{1}{3}
> $$
✔ Answer: $ \frac{1}{3} $
---
3. What is the probability of rolling less than 5?
Numbers less than 5:
1, 2, 3, 4
- Favorable outcomes: 4 numbers
> $$
> \text{Probability} = \frac{4}{6} = \frac{2}{3}
> $$
✔ Answer: $ \frac{2}{3} $
---
4. What is the probability of rolling an even number?
Even numbers on a die:
2, 4, 6
- Favorable outcomes: 3
> $$
> \text{Probability} = \frac{3}{6} = \frac{1}{2}
> $$
✔ Answer: $ \frac{1}{2} $
---
5. What is the probability of rolling an odd number?
Odd numbers:
1, 3, 5
- Favorable outcomes: 3
> $$
> \text{Probability} = \frac{3}{6} = \frac{1}{2}
> $$
✔ Answer: $ \frac{1}{2} $
---
6. What is the probability of rolling a prime number?
First, recall:
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.
Numbers on a die: 1, 2, 3, 4, 5, 6
Check which are prime:
- 1 → not prime
- 2 → prime
- 3 → prime
- 4 → not prime (divisible by 2)
- 5 → prime
- 6 → not prime (divisible by 2 and 3)
So prime numbers:
2, 3, 5 → 3 outcomes
> $$
> \text{Probability} = \frac{3}{6} = \frac{1}{2}
> $$
✔ Answer: $ \frac{1}{2} $
*(Note: The hint says "Remember: 1 is not a prime number" — correct!)*
---
7. What is the probability of rolling a 3 or a 6?
Favorable outcomes: 3 or 6 → 2 outcomes
> $$
> \text{Probability} = \frac{2}{6} = \frac{1}{3}
> $$
✔ Answer: $ \frac{1}{3} $
---
8. What is the probability of rolling an even prime number?
Let’s think: Which numbers are
even and
prime?
Even numbers: 2, 4, 6
Which of these are prime?
- 2 → prime
✔
- 4 → not prime
- 6 → not prime
Only
2 is an even prime number.
So only one favorable outcome: 2
> $$
> \text{Probability} = \frac{1}{6}
> $$
✔ Answer: $ \frac{1}{6} $
---
✔ Final Answers:
1. $ \frac{1}{6} $
2. $ \frac{1}{3} $
3. $ \frac{2}{3} $
4. $ \frac{1}{2} $
5. $ \frac{1}{2} $
6. $ \frac{1}{2} $
7. $ \frac{1}{3} $
8. $ \frac{1}{6} $
Let me know if you'd like this formatted as a printable worksheet or need explanations in simpler terms!
Parent Tip: Review the logic above to help your child master the concept of simple probability worksheet.
