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…

Explanation:

Step1: Find total possible outcomes

When rolling two number - cubes (dice), each die has 6 faces. So the total number of possible outcomes is (6\times6 = 36).

Step2: Find number of ways to roll a 9

The possible combinations to get a sum of 9 on two dice are ((3,6)), ((4,5)), ((5,4)), ((6,3)). So there are 4 ways to roll a 9.

Step3: Calculate probability of rolling a 9

The probability (P(9)) of rolling a 9 is (\frac{4}{36}=\frac{1}{9}).

Step4: Find number of ways to roll a 6

The possible combinations to get a 6 on two dice are ((1,5)), ((2,4)), ((3,3)), ((4,2)), ((5,1)). So there are 5 ways to roll a 6.

Step5: Calculate probability of rolling a 6

The probability (P(6)) of rolling a 6 is (\frac{5}{36}).

Step6: Compare probabilities

Since (\frac{5}{36}>\frac{1}{9}=\frac{4}{36}), Alex is more likely to win.

Answer:

Alex is more likely to win because the probability of rolling a 6 on two number - cubes ((\frac{5}{36})) is greater than the probability of rolling a total of 9 on two number - cubes ((\frac{4}{36})).