Question

Select the correct answer from each drop-down menu. A dice game involves rolling two dice. A player who rolls a 3, 4, 10, 11, or 12 wins 5 points. A player who rolls a 5, 6, 7, 8, or 9 loses 5 points. If the expected value of playing this game is to lose, a player will ______ points by rolling a 2.

1) gain
2) lose
3) neither gain nor lose
4) cannot be determined

Answer 1

The expected value of rolling a 2 in the dice game cannot be determined without knowing the corresponding points gained or lost.

Step-by-step explanation:

The expected value of playing a game can be calculated by multiplying the value of each outcome by its probability, and summing those values. In this case, the player wins 5 points if they roll a 3, 4, 10, 11, or 12, and loses 5 points if they roll a 5, 6, 7, 8, or 9. To determine the expected value of rolling a 2, we need to know the probability of rolling a 2 and the corresponding points gained or lost. Since the question does not provide this information, the answer cannot be determined.