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A single die is rolled twice. The equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is . The probability of getting two numbers whose sum is is . (Type an integer or a simplified fraction.)
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Q. A single die is rolled twice. The equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is . The probability of getting two numbers whose sum is is . (Type an integer or a simplified fraction.)
- Identify Possible Outcomes: First, we need to identify all the possible outcomes when rolling two dice that result in a sum of . The pairs are , , , , and . Each pair represents a different outcome where the sum of the two dice is .
- Count Outcomes: Next, we count the number of outcomes that result in a sum of . There are such outcomes as identified in the previous step.
- Determine Total Possibilities: Now, we need to determine the total number of possible outcomes when rolling two dice. Since each die has faces, and each face is equally likely, there are possible outcomes.
- Calculate Probability: To find the probability of getting a sum of , we divide the number of outcomes that give us a sum of by the total number of possible outcomes. So, the probability is .
