Two different colored dice are rolled simultaneously.What is the probability of getting a sum of at least 3?Write your answer as a simplified fraction.
Question
Two different colored dice are rolled simultaneously.
What is the probability of getting a sum of at least 3?
Write your answer as a simplified fraction.
Solution
When two dice are rolled, there are a total of 6*6 = 36 possible outcomes.
The only sums that are less than 3 when two dice are rolled are 1 and 2.
1 can only be achieved by rolling a 1 on both dice, and 2 can be achieved by rolling a 1 on one die and a 2 on the other, or vice versa.
So there are 1 + 2 = 3 outcomes where the sum is less than 3.
Therefore, the number of outcomes where the sum is at least 3 is 36 - 3 = 33.
So the probability of getting a sum of at least 3 is 33/36, which simplifies to 11/12.
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