### Instruction: If Michael rolls three fair dice, what is the probability that he will roll at least two 1's? Express your answer as a common fraction.### Response: I know that the probability of rolling a 1 on one die is 1/6, and the probability of rolling something else is 5/6.
If I want to roll at least two 1's, I can either roll exactly two 1's and something else, or roll all three 1's.
To roll exactly two 1's and something else, I can choose which die is not 1 in three ways, and then multiply the probabilities of each outcome: 3 * (1/6) * (1/6) * (5/6) = 15/216.
To roll all three 1's, I just multiply the probabilities of each outcome: (1/6) * (1/6) * (1/6) = 1/216.
To get the total probability of rolling at least two 1's, I add these two cases: 15/216 + 1/216 = 16/216.
I can simplify this fraction by dividing the numerator and denominator by 8: 16/216 = 2/27.