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You roll all three dice at once. Can any of you Masters of the Black Arts of Probability tell this innumerate moron the odds of the following results occurring?

1) The special die is one of the two highest dice (i.e., 6,

2) The two highest dice are a pair, and the special die is one of them (i.e., 5,

3) The two highest dice are a pair, and the special die is

4) There's a pair, the special die is one of them, but another die is higher (i.e., 1,

5) There's a pair, but the special die is both higher and not part of the pair (i.e., 2, 2,

Thanks in advance!

## Comments

4" qualify?1) About 74.5% = (1*1 + 2*3 + 3*5 + 4*7 + 5*9 + 6*11) / 6^3

2) About 16.7% = 1/6

3) About 6.9% = (5 + 4 + 3 + 2 + 1 + 0) / 6^3

4) About 13.9% = 5/36

5) About 6.9% = (5 + 4 + 3 + 2 + 1 + 0) / 6^3

Can someone check my maths here?

-JT

Two other stats that weren't asked for:

The chance of getting any pair (whether the special is part of them or not): 44.4%

There's a pair, and the special isn't one of them (it's higher OR lower): 13.9%