Question

You roll a 6-sided die two times.




What is the probability of rolling a prime number and then rolling a number greater than 3?

Write your answer as a percentage.

Answer 1

To solve the problem, we first need to identify the prime numbers on a 6-sided die and the numbers greater than 3.

The prime numbers on a 6-sided die (which has the faces numbered 1 to 6) are:
- 2
- 3
- 5

So, there are 3 prime numbers.

The numbers greater than 3 on a 6-sided die are:
- 4
- 5
- 6

So, there are 3 numbers greater than 3.

Next, we calculate the probability of each event:

1. **Probability of rolling a prime number**:
The total outcomes for a single die roll is 6. Therefore, the probability of rolling a prime number is:
\[
P(\text{prime}) = \frac{\text{Number of prime numbers}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]

2. **Probability of rolling a number greater than 3**:
Similarly, the probability of rolling a number greater than 3 is:
\[
P(\text{greater than 3}) = \frac{\text{Number of outcomes greater than 3}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]

Since the two rolls are independent, we can multiply the probabilities:
\[
P(\text{prime and greater than 3}) = P(\text{prime}) \times P(\text{greater than 3}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\]

To express this as a percentage:
\[
\frac{1}{4} \times 100\% = 25\%
\]

Thus, the probability of rolling a prime number and then rolling a number greater than 3 is **25%**.