When two dice are thrown, then total outcome = 36

1. Sum of 9: {(3, 6), (4, 5), (5, 4), (6, 3)}

Favourable outcome = 4

So, P(A total of 9) = 4/36 = 1/9

2. Two ones: (1, 1)

Favourable outcome = 1

So, P(Two ones) = 1/36

3. At least one 6: {(1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Favourable outcome = 11

So, P(Two ones) = 11/36

4. Sum of 9: {(3, 6), (4, 5), (5, 4), (6, 3)}

    Sum of 11: {(5, 6), (6, 5)}

Favourable outcome = 4 + 2 = 6

So, P(A sum of 9 or 11) = 6/36 = 1/6

5. A sum of at least 10: {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

Favourable outcome = 6

So, P(A sum of at least 10) = 6/36 = 1/6

6. A sum as a prime number: {(1,1), (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (4,1), (4,3), (5,2), (5,6), (6,1), (6,5)}

Favourable outcome = 15

So, P(A sum as a prime number) = 15/36 = 5/12