predicting the winner\nyou must roll a total of 9 on two number cubes to win the game. alex must roll a 6…

predicting the winner\nyou 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.

predicting the winner\nyou 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.

Answer

Explanation:

Step1: Find total number of outcomes

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

Step2: Find number of ways to get a sum of 9

The pairs of numbers on the two cubes that sum to 9 are ((3,6)), ((4,5)), ((5,4)), ((6,3)). So there are 4 ways to get a sum of 9. The probability of getting a sum of 9, (P(9)=\frac{4}{36}=\frac{1}{9}).

Step3: Find number of ways to get a sum of 6

The pairs of numbers on the two cubes that sum to 6 are ((1,5)), ((2,4)), ((3,3)), ((4,2)), ((5,1)). So there are 5 ways to get a sum of 6. The probability of getting a sum of 6, (P(6)=\frac{5}{36}).

Step4: 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 9 on two number - cubes ((\frac{4}{36})).