Question

sample response: 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. check all that you considered in your response. the probability of getting a 9 is 4/36 the probability of getting a 6 is 5/36. 5/36 is greater than 4/36, so it is more likely that a 6 will be rolled.

Explanation:

Step1: Determine total outcomes

When rolling two - dice, the total number of outcomes is $6\times6 = 36$ since each die has 6 faces.

Step2: Calculate probability of rolling a 9

There are 4 combinations to roll a 9: (3,6), (6,3), (4,5), (5,4). So the probability of rolling a 9 is $\frac{4}{36}$.

Step3: Calculate probability of rolling a 6

There are 5 combinations to roll a 6: (1,5), (5,1), (2,4), (4,2), (3,3). So the probability of rolling a 6 is $\frac{5}{36}$.

Step4: Compare probabilities

Since $\frac{5}{36}>\frac{4}{36}$, it is more likely to roll a 6.

Answer:

The probability of getting a 9 is 4/36, The probability of getting a 6 is 5/36, 5/36 is greater than 4/36, so it is more likely that a 6 will be rolled.