To solve these probability problems, we first need to understand the possible outcomes when tossing a fair die.
A standard die has 6 faces with the numbers:
1, 2, 3, 4, 5, 6.
So, the total number of possible outcomes is
6.
The probability of an event is calculated as:
$$ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} $$
Let's go through each question step by step.
1. What is the probability of rolling a 3?
- Favorable outcome: Rolling a 3. There is only
1 face with a 3.
- Total outcomes: 6.
- Probability: $\frac{1}{6}$
2. What is the probability of rolling more than 4?
- "More than 4" means numbers strictly greater than 4.
- The numbers on the die greater than 4 are:
5, 6.
- Number of favorable outcomes:
2.
- Probability: $\frac{2}{6}$
- Simplify the fraction: Divide top and bottom by 2 → $\frac{1}{3}$
3. What is the probability of rolling less than 5?
- "Less than 5" means numbers strictly smaller than 5.
- The numbers on the die less than 5 are:
1, 2, 3, 4.
- Number of favorable outcomes:
4.
- Probability: $\frac{4}{6}$
- Simplify the fraction: Divide top and bottom by 2 → $\frac{2}{3}$
4. What is the probability of rolling an even number?
- Even numbers are divisible by 2.
- The even numbers on the die are:
2, 4, 6.
- Number of favorable outcomes:
3.
- Probability: $\frac{3}{6}$
- Simplify the fraction: Divide top and bottom by 3 → $\frac{1}{2}$
5. What is the probability of rolling an odd number?
- Odd numbers are not divisible by 2.
- The odd numbers on the die are:
1, 3, 5.
- Number of favorable outcomes:
3.
- Probability: $\frac{3}{6}$
- Simplify the fraction: Divide top and bottom by 3 → $\frac{1}{2}$
6. What is the probability of rolling a prime number?
- A prime number is a number greater than 1 that has no divisors other than 1 and itself.
- Let's check the numbers on the die:
- 1 is
not prime (by definition).
- 2 is prime.
- 3 is prime.
- 4 is not prime ($2 \times 2$).
- 5 is prime.
- 6 is not prime ($2 \times 3$).
- The prime numbers are:
2, 3, 5.
- Number of favorable outcomes:
3.
- Probability: $\frac{3}{6}$
- Simplify the fraction: Divide top and bottom by 3 → $\frac{1}{2}$
7. What is the probability of rolling a 3 or a 6?
- Favorable outcomes: Rolling a 3 OR rolling a 6.
- The numbers are:
3, 6.
- Number of favorable outcomes:
2.
- Probability: $\frac{2}{6}$
- Simplify the fraction: Divide top and bottom by 2 → $\frac{1}{3}$
8. What is the probability of rolling an even prime number?
- We listed the prime numbers in question 6:
2, 3, 5.
- Among these, which ones are even?
- 2 is even.
- 3 is odd.
- 5 is odd.
- So, the only even prime number is
2.
- Number of favorable outcomes:
1.
- Probability: $\frac{1}{6}$
Final Answer:
1. 1/6
2. 1/3
3. 2/3
4. 1/2
5. 1/2
6. 1/2
7. 1/3
8. 1/6
Parent Tip: Review the logic above to help your child master the concept of experimental probability worksheet 7th grade.
