1. **State the problem:** We want to find the probability of getting no prime numbers when two dice are thrown. 2. **Identify prime numbers on a die:** The numbers on a die are 1, 2, 3, 4, 5, 6. The prime numbers here are 2, 3, and 5. 3. **Calculate the probability of no prime number on one die:** The non-prime numbers are 1, 4, and 6. So, the probability of getting a non-prime number on one die is $\frac{3}{6} = \frac{1}{2}$. 4. **Calculate the probability of no prime numbers on two dice:** Since the dice rolls are independent, multiply the probabilities: $$\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$$ 5. **Final answer:** The probability of getting no prime numbers when two dice are thrown is $\frac{1}{4}$ or 0.25.