Question

In the dice rolling game, what amount does a player win if the sum is 2 or 12?

A) $4
B) $12
C) $1.50
D) Nothing

Answer 1

In the dice rolling game, the amount does a player win if the sum is 2 or 12 is D) Nothing.

Step-by-step explanation:

In the dice rolling game, the sum of 2 or 12 occurs when two six-sided dice show a 1 and 1 or a 6 and 6, respectively. Since there is only one combination for each of these outcomes, the probability of rolling a sum of 2 or 12 is
`\( (1)/(36) \)` for each case. To determine the expected value, we multiply the probability of each outcome by the corresponding amount won or lost.

For a sum of 2, the player would theoretically win an amount, but the given options don't specify a monetary reward for this specific result. Therefore, the player wins nothing for rolling a 2. The same reasoning applies to a sum of 12. In both cases, the probability of occurrence is low, and there is no indicated prize for these outcomes in the provided choices.

Mathematically, the expected value (E) is calculated as the sum of each outcome's probability multiplied by its associated amount:

`\[ E = P(\text{Sum of 2}) * \text{Amount for Sum of 2} + P(\text{Sum of 12}) * \text{Amount for Sum of 12} \]`

Substituting in the probabilities and amounts, we get:

`\[ E = (1)/(36) * 0 + (1)/(36) * 0 = 0 \]`

Thus, the player does not win any amount for rolling a sum of 2 or 12 in this dice rolling game.

So the correct answer is D) Nothing