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:
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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: \[ P(\text{prime}) = \frac{\text{Number of prime numbers}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} \]
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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%.