# A fair 2

A fair die is thrown two times. What is the probability that the sum of the score is almost 8?

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**Math student**

By "almost 8", did you mean "at most 8"?

It's appropriate, in your solution, to double the number of ways to get a total of at most 8 on different outcomes, but it's not appropriate to double the number of times you roll doubles (so 1+1, 2+2, 3+3, 4+4). Therefore, your 30/36 figure over-counts by 4. The correct answer is 26/36. Another way to reach this is to look at a 6-by-6 grid of ordered pairs: (1,1) through (6,6). Diagonals have a constant sum: 1 way to roll 2, 2 ways to roll 3, ..., 6 ways to roll 7, 5 ways to roll 8. Answer: (1+2+3+4+5+6+5)/36=26/36.

It's appropriate, in your solution, to double the number of ways to get a total of at most 8 on different outcomes, but it's not appropriate to double the number of times you roll doubles (so 1+1, 2+2, 3+3, 4+4). Therefore, your 30/36 figure over-counts by 4. The correct answer is 26/36. Another way to reach this is to look at a 6-by-6 grid of ordered pairs: (1,1) through (6,6). Diagonals have a constant sum: 1 way to roll 2, 2 ways to roll 3, ..., 6 ways to roll 7, 5 ways to roll 8. Answer: (1+2+3+4+5+6+5)/36=26/36.

10 months ago 3 Likes

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