Math Bell Ringer for Grades 9–12: Comparing two-dice probabilities
A free math bell ringer for grades 9–12. Put the prompt on the board as students walk in, give them three to five minutes, then go over it together. The answer and teacher notes are in the box below the prompt.
The prompt
You roll two fair six-sided dice and add the numbers. Which is more likely: a sum of 7 or a sum of 10? Give the probability of each as a fraction in lowest terms.
Answer and teacher notes
There are 6 × 6 = 36 equally likely outcomes.
Sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes, so 6/36 = 1/6.
Sum of 10: (4,6), (5,5), (6,4) = 3 outcomes, so 3/36 = 1/12.
A sum of 7 is twice as likely as a sum of 10. Check: 1/6 = 2/12. The most common error is counting (4,6) and (6,4) as the same outcome; on two separate dice they are different.
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