### Instruction: Two standard dice are rolled. What is the expected number of 1's obtained? Express your answer as a common fraction.### Response: To find the expected number of 1's, I need to multiply the probability of getting a 1 on each die by the number of 1's that would result.
For the first die, the probability of getting a 1 is 1/6, and the number of 1's is 1, so the contribution from the first die is (1/6) * 1 = 1/6.
For the second die, the probability of getting a 1 is also 1/6, and the number of 1's is 1, so the contribution from the second die is (1/6) * 1 = 1/6.
To get the total expected number of 1's, I need to add the contributions from both dice.
So the expected number of 1's is 1/6 + 1/6 = 2/6 = 1/3.