Prove that in throwing a pair of dice, the occurrence of the number 4 on the first die is independent of the occurrence of 5 on the second die.

Explanation

To prove that the occurrence of the number 4 on the first die is independent of the occurrence of 5 on the second die, we will use the definition of independent events in probability. Two events A and B are independent if:

\[ P(A \cap B) = P(A) \times P(B) \]

### Step-by-Step Solution:

1. **Define the Events**:
- Let event A be the occurrence of the number 4 on the first die.
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