Question

The sums that appear when two fair? four-sided dice? (tetrahedrons) with sides 1?, 2?, 3?, and 4 are tossed

Answer 1

Answer:

The possible sums are 2, 3, 4, 5, 6, 7 & 8 (but they're not all equally likely)

Step-by-step explanation:

For example, the only way to get a sum of 2 is to roll a 1 and then a 1

And the only way to get a sum of 8 is to roll a 4 and then a 4 (imagine you don't roll the two dice simultaneously; this will help you to see the "other possibilities" that aren't obvious at first)

The probability of rolling a sum of 2 = probability of rolling sum of 8 (1/16 probability for each)

If you roll a 1 then a 2, or a 2 then a 1, there are 2 ways to get a sum of 3

If you roll a 3 then a 1, a 2 then a 2, or a 1 then a 3, there are 3 ways to get a sum of 4

If you roll a 4 then a 1, a 3 then a 2, a 2 then a 3, or a 1 then a 4, there are 4 ways to get a sum of 5 (5 is the most likely sum)

If you roll a 4 then a 2, a 3 then a 3, or a 2 then a 4, there are 3 ways to get a sum of 6

If you roll a 4 then a 3, or a 3 then a 4, there are 2 ways to get a sum of 7