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.

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

Answered by nlindroth858 | 2024-06-25

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 36 6 ​ or 6 1 ​ chance of getting exactly 6
While 9 has 4 combinations 3+6 4+5 5+4 6+3 So you have 36 4 ​ or 9 1 ​ chance of getting exactly 9
So Alex has a better chance

Answered by Geekhawk | 2024-06-25

Alex has a probability of 6 1 ​ to roll a 6, while the probability of the other player rolling a total of 9 is 9 1 ​ . Since 6 1 ​ is greater than 9 1 ​ , Alex is more likely to win. Therefore, Alex has the better chance to win on the next turn.
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Answered by Geekhawk | 2024-09-05