Give an example of an event that is more likely than rolling a sum of 8

Question

saiyansruleA · Accepted Answer

The outcomes for each number cube are 1, 2, 3, 4, 5, and 6 so the smallest possible sum for two number cubes is

$1 + 1 = 2$

and the largest possible sum is

$6 + 6 = 12.$
The outcomes for rolling a sum of 8 are

$2 + 62 + 6$ ,

$6 + 26 + 2$ ,

$3 + 53 + 5$ ,

$5 + 35 + 3$ ,

and

$4 + 4$ .

There are then 5 possible outcomes for rolling a sum of 8.
If an event has more than 5 possible outcomes, it would then be more likely than rolling a sum of 8.
The smaller the sum is (such as a sum of 3 or 4) or the larger the sum is (such as a sum of 10 or 11), the fewer possible outcomes there are.
The sum with the largest number of possible outcomes is then the sum halfway between the smallest sum of 2 and the largest sum of 12, which is

$\frac{2 + 12}{2} = \frac{14}{2} = 7$
The possible outcomes for a sum of 7 are

$1 + 6$ ,

$6 + 1$ ,

$2 + 5$ ,

$5 + 2$ ,

$3 + 4$ ,

and

$4 + 3$

so there are 6 possible outcomes for a sum of 7. There are then more possible outcomes for a sum of 7 than there are for a sum of 8.
An event that is more likely than rolling a sum of 8 is then rolling a sum of 7.

Give an example of an event that is more likely than rolling a sum of 8

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