Answer :
Answer: 15 different ways
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Explanation:
I'll use ordered pair notation to indicate the dice results. I'll have blue go first, then yellow second. Something like (6,3) means that blue got 6 while yellow got 3. Another example of (5,2) means the blue die shows 5 while the yellow one shows 2.
Now let's say the blue die rolls to show "1". Is it possible for the blue die to have a larger value than the yellow die? The answer is "no" because it's not possible to roll 0 on the yellow die, and we can't roll negative values either. This means that if we want the blue die to show a value larger than the yellow die, then it must be larger than 1.
If the blue die shows "2", then the only outcome to fit the description is to have the yellow die show "1". We write that as the ordered pair (2,1). Writing (1,2) is the other way around so we'll ignore that. Any other value on the yellow die is not possible since something like (2,5) does not fit the conditions given to us.
If the blue die shows "3", then we could have (3,1) or (3,2) that fit the conditions that the blue die is larger than the yellow one. We have two cases here compared to the one earlier.
If the blue die shows "4", then we could have (4,1) or (4,2) or (4,3). We have three cases here.
You can probably spot the pattern:
- We have one case if the blue die shows "2"
- We have two cases if the blue die shows "3"
- We have three cases if the blue die shows "4"
and so on. The number of cases is one less than whatever the blue die value is showing. Overall we have 1+2+3+4+5 = 15 possible ways to have the blue die be a larger value than the yellow die. Use of a dice chart is handy to help confirm the answer.