Question

Dustin and Melanie are playing a game with two standard, six-sided number cubes. Dustin guesses a sum of six, and Melanie guesses a sum of seven. Which player made the better decision?

a) Dustin
b) Melanie
c) Both made equally good decisions
d) Cannot be determined

Answer 1

Both Dustin and Melanie made equally good decisions as their guesses have different probabilities but equal possibilities.

Step-by-step explanation:

Both Dustin and Melanie made equally good decisions. To determine this, we need to analyze the possible outcomes of the sum of two dice. There are a total of 36 possible outcomes when two standard, six-sided dice are rolled, since each die has 6 possible outcomes.

For Dustin's guess of a sum of six, there are 5 possible outcomes (1+5, 2+4, 3+3, 4+2, 5+1) out of 36. Therefore, the probability of rolling a sum of six is 5/36.

For Melanie's guess of a sum of seven, there are 6 possible outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36. Therefore, the probability of rolling a sum of seven is 6/36.

Since both guesses have different probabilities but equal possibilities, they both made equally good decisions.