Subjects probability

Sum Seven 8206C4

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1. **State the problem:** We need to find the probability that the sum of the numbers on two fair dice is 7 when both are tossed once. 2. **Formula for probability:** Probability of an event = \frac{Number of favorable outcomes}{Total number of possible outcomes} 3. **Total possible outcomes:** Each die has 6 faces, so total outcomes when tossing two dice = $6 \times 6 = 36$ 4. **Favorable outcomes for sum 7:** The pairs that sum to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). There are 6 such pairs. 5. **Calculate probability:** $$ P(\text{sum} = 7) = \frac{6}{36} = \frac{\cancel{6}}{\cancel{36}} = \frac{1}{6} $$ 6. **Final answer:** The probability that the sum is 7 in a single toss of two fair dice is $\boxed{\frac{1}{6}}$.