Determine whether the players have equal probabilities of winning.
-Toss two fair dice numbered 1 through 6. If the sum is 7, player 1 wins; if the sum is 3 or 4, player 2 wins.
A)Yes
B)No

Question

Quizplus · Accepted Answer

The probabilities are not equal. For player 1 to win, the sum must be 7, which can occur in 6 out of 36 possible outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). For player 2 to win, the sum must be 3 or 4, which can occur in 3 out of 36 outcomes for a sum of 3 (1+2, 2+1) and 3 out of 36 outcomes for a sum of 4 (1+3, 2+2, 3+1), totaling 6 out of 36 possible outcomes. Therefore, each player has an equal chance of winning, contradicting my initial conclusion. The correct interpretation should be that both players indeed have equal probabilities of winning, as each set of winning conditions occurs in 6 out of 36 possible outcomes.

Determine Whether the Players Have Equal Probabilities of Winning