13. If a pair of 6-faced dice is rolled, what sum of the two numbers are you most likely to get:
a. 9
b. 12
c. 7
d. 8
When rolling a pair of fair 6-faced dice, the most likely sum is 7, occurring in 6 out of 36 possible outcomes for a probability of 636=16 [execute_python].
Total Outcomes
Two dice produce 36 equally likely outcomes, as each die shows faces 1 through 6. Sums range from 2 to 12, with frequencies peaking at 7 (6 ways), followed by 6 and 8 (5 ways each), 5 and 9 (4 ways each), 4 and 10 (3 ways each), 3 and 11 (2 ways each), and extremes 2 and 12 (1 way each) [execute_python].
Option Analysis
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a. 9: Four outcomes yield sum 9 ((3,6), (4,5), (5,4), (6,3)), so probability 436=19≈0.1111. Less likely than 7 [execute_python].
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b. 12: Only one outcome ((6,6)), probability 136≈0.0278. Least likely among options [execute_python].
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c. 7: Six outcomes ((1,6), (2,5), (3,4), (4,3), (5,2), (6,1)), highest probability 636=16≈0.1667 [execute_python].
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d. 8: Five outcomes ((2,6), (3,5), (4,4), (5,3), (6,2)), probability 536≈0.1389. Second most likely but trails 7 [execute_python].
Probability Comparison
| Sum | Ways | Probability |
|---|---|---|
| 7 | 6 | 636 [execute_python] |
| 8 | 5 | 536 [execute_python] |
| 9 | 4 | 436 [execute_python] |
| 12 | 1 | 136 [execute_python] |
The correct choice is c. 7, ideal for probability questions
