Will someone please double-check my work on Rukar? Was not working with known formulas, just logic.

R. RUKAR

1. 0 damage: 3.7%

2. 1 damage: 5.6%

- Probability of one hit is 22.2%

- Probability of hit being six is 25%

- Product of both probabilities: 5.6%

3. 2 damage: 30.6%

One six-hit and two misses: 5.6%

- Probability of rolling 1 hit out of 3 dice: 22.2%

- Probability 1 hit will be a 6: 25%

- Product of both is 5.6%

Two non-six hits and one miss:

- Probability of two hits is 44.4%

- Probability both hits will not be a six: 56.3%

- Product of both is: 25%

Sum of above two products is 30.6%

4. 3 damage: 29.2%

Probability of two hits is 2: 44.4%

Probability one of those two will be a 6: 37.5

Product of those two numbers is 16.7%

Probability of 3 hits is 29.6%

Probability all 3 are not sixes is 42.2

Product of those two numbers is 12.5%

Sum of those two products is 29.2%

5. 4 damage: 15.3%

Probability of two hits is 2: 44.4%

Probability both dice will be sixes: 6.3%

Product of those two probabilities is: 2.8%

Probability three hits is: 29.6%

Probability one out of three is a six is: 42.2%

Product of those two probabilities: 12.5

Sum of two products is 15.3%

6. 5 damage: 12.4%

Probability of three hits is 29.6%

Probability one of three hits will be a six: 42%

Product of those two probabilities is: 12.4%

6. 6 damage0.5%

My total probabilities sum comes up to 102.7: not sure if that's just because I rounded all tenths up.