rymatson406 said:We roll a pair of dice. If the sum of the dice is 7, you pay me $28. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is the price that you should pay to play the game that would make the game fair?
The expected value of rolling a pair of dice is 7. This means that if you were to roll the dice an infinite number of times, you can expect the average value to be 7.
The expected value is calculated by multiplying the probability of each outcome by its corresponding value, and then adding all of these products together. For rolling a pair of dice, there are 36 possible outcomes and each outcome has a probability of 1/36. Therefore, the expected value is (1/36)*(2+3+4+5+6+7+8+9+10+11+12) = 7.
The expected value is important because it helps us understand the average outcome of a random event. In the case of rolling a pair of dice, it can help us determine if a game is fair or not. For example, if someone wants to charge you $10 to play a game where you roll a pair of dice and win $12 if you roll a 7, you can calculate the expected value to see if it is a fair price to play.
No, the expected value can vary depending on the rules of the game. For example, if the game has a different payout for rolling a 7, the expected value will be different. However, for a fair game where the payout for rolling a 7 is equal to the cost of playing, the expected value will always be 7.
The fair price to play a game of rolling a pair of dice with an expected value of 7 would be $7. This means that if you were to play the game an infinite number of times, you can expect to break even. Any price lower than $7 would be considered a good deal, while any price higher would be considered a bad deal.