select the correct answer from the drop - down menu. dustin and melanie are playing a game where they roll 2…

select the correct answer from the drop - down menu. dustin and melanie are playing a game where they roll 2 standard 6 - sided number cubes and find the sum of their outcomes. each player gets a chance to guess the correct sum, and the player who guesses the correct sum wins the game. dustin decides to guess a sum of 6. melanie decides to guess a sum of 7. which player made the better decision?

select the correct answer from the drop - down menu. dustin and melanie are playing a game where they roll 2 standard 6 - sided number cubes and find the sum of their outcomes. each player gets a chance to guess the correct sum, and the player who guesses the correct sum wins the game. dustin decides to guess a sum of 6. melanie decides to guess a sum of 7. which player made the better decision?

Answer

Explanation:

Step1: Find total number of outcomes

When rolling two 6 - sided dice, the total number of outcomes is $6\times6 = 36$.

Step2: Find number of ways to get a sum of 6

The possible combinations for a sum of 6 are $(1,5),(2,4),(3,3),(4,2),(5,1)$, so there are 5 ways.

Step3: Find number of ways to get a sum of 7

The possible combinations for a sum of 7 are $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$, so there are 6 ways.

Step4: Compare probabilities

The probability of getting a sum of 6 is $\frac{5}{36}$, and the probability of getting a sum of 7 is $\frac{6}{36}$. Since $\frac{6}{36}>\frac{5}{36}$, Melanie has a higher - probability of winning.

Answer:

Melanie