Question

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?

Explanation:

Step1: Find total outcomes

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

Step2: Find outcomes for sum = 6

The pairs that sum to 6 are: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1). So there are 5 outcomes. The probability of Dustin's guess (sum = 6) is $\frac{5}{36}$.

Step3: Find outcomes for sum = 7

The pairs that sum to 7 are: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). So there are 6 outcomes. The probability of Melanie's guess (sum = 7) is $\frac{6}{36}=\frac{1}{6}$.

Step4: Compare probabilities

Since $\frac{6}{36}>\frac{5}{36}$ (or $\frac{1}{6}>\frac{5}{36}$), Melanie's guess has a higher probability of being correct. So Melanie made the better decision.

Answer:

Melanie