amazingphil
Answered

Please help!

You must roll a total of 9 on two number cubes to win the game. Alex must roll a 6. Who is more likely to win the game on the next turn? Explain.

Verified Answer :

Geekhawk

There are 36 possible combinations for 2 dices because there are 6 numbers per di
6 has 5 combinations because you must use 2 dices
1+5
2+4
3+3
4+3
5+1
So Alex has \(\frac{6}{36}\) or \(\frac{1}{6}\) chance of getting exactly 6

While 9 has 4 combinations
3+6
4+5
5+4
6+3
So you have \(\frac{4}{36}\) or \(\frac{1}{9}\) chance of getting exactly 9

So Alex has a better chance

To roll a 9, you need a combination of 3 and 6, or 4 and 5, in any order. To roll a 6, Alex needs a combination of 1 and 5, 2 and 4, or 3 and 3, in any order. There are 4 possible ways to roll a 9 and 5 possible ways to roll a 6, so Alex is more likely to win