Half Betting

What are the odds of rolling a six with a standard die if you have three chances?

I know the odds of rolling a six with one die is 1/6. My odds go up if I have three chances. I assume I need to calculate all possible roll combinations and then subtract those containing a six. What is the formula?

Public Comments

1. Binomial probability. p(rolling a six) = 1/6. p(rolling exactly one 6 in 3 rolls) = [3C2] * (1/6)^1 * (5/6)^2 = 3 * (1/6) * (25/36) = 75/216 = 0.3472. p(roll at least one 6 in 3 rolls) = 1 - p(rolling no sixes) = 1 - (5/6)^3 = 0.4213.