Probability of getting a sum divisible by 4 when a die is thrown twice:

To find the probability of getting a sum divisible by 4 when a die is thrown twice, we first need to determine all the possible outcomes and then count the favorable outcomes.

1. Determining all possible outcomes:

When a die is thrown twice, there are a total of 6 outcomes for each throw. Therefore, the total number of possible outcomes for two throws is 6 * 6 = 36.

2. Counting favorable outcomes:

To determine the favorable outcomes, we need to find all the combinations of numbers that add up to a sum divisible by 4. Let's consider all the possible combinations:

- (1, 3): The sum is 4, which is divisible by 4.
- (1, 4): The sum is 5, which is not divisible by 4.
- (1, 5): The sum is 6, which is not divisible by 4.
- (1, 6): The sum is 7, which is not divisible by 4.

- (2, 2): The sum is 4, which is divisible by 4.
- (2, 3): The sum is 5, which is not divisible by 4.
- (2, 4): The sum is 6, which is not divisible by 4.
- (2, 5): The sum is 7, which is not divisible by 4.
- (2, 6): The sum is 8, which is not divisible by 4.

- (3, 1): The sum is 4, which is divisible by 4.
- (3, 2): The sum is 5, which is not divisible by 4.
- (3, 3): The sum is 6, which is not divisible by 4.
- (3, 4): The sum is 7, which is not divisible by 4.
- (3, 5): The sum is 8, which is not divisible by 4.
- (3, 6): The sum is 9, which is not divisible by 4.

- (4, 1): The sum is 5, which is not divisible by 4.
- (4, 2): The sum is 6, which is not divisible by 4.
- (4, 3): The sum is 7, which is not divisible by 4.
- (4, 4): The sum is 8, which is not divisible by 4.
- (4, 5): The sum is 9, which is not divisible by 4.
- (4, 6): The sum is 10, which is not divisible by 4.

- (5, 1): The sum is 6, which is not divisible by 4.
- (5, 2): The sum is 7, which is not divisible by 4.
- (5, 3): The sum is 8, which is not divisible by 4.
- (5, 4): The sum is 9, which is not divisible by 4.
- (5, 5): The sum is 10, which is not divisible by 4.
- (5,