Suppose that in a particular game two dice are tossed, and various amounts are paid according to the outcome. Find the requested probability. (Enter the probability as a fraction.) If a seven or an eight occurs on the first roll, the player wins. What is the probability of winning on the first roll?

Question

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Answer 1

36 possible outcomes if order matters

If it is the sum that matters you have to figure a different probability for every sum
for example there are 4 ways of getting a sum of 5
1+4 or 4+1
2+3 or 3+2
to get a sum of 6 though, there are 5 ways
1+5 or 5+1
2+4 or 4+2
3+3
On the first roll
get 7 with
1+6 or 6+1
2+5 or 5+2
3+4 or 4+3
four ways so 4/36 = 1/9
get 8 with
2+6 or 6+2
3+5 or 5+3
4+4
five ways so 5/36

1/9 + 5/36 = 9/36 = 1/4 = chance of winning on first roll

Answer 2

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