Question

Game of doubles (when the outcome on two simultaneously rolled dice is the same) is modified such that a player who gets 3 or more doubles in 5 rolls (that is, the player rolls two dice simultaneously in a sequence five times ends up with three or more doubles in the five rolls) wins $30. the cost of each round of 5 rolls is $1 (that is, for $1 you get to roll the dice five times). should you play the game?

Answer 1

To determine whether or not you should play the game, calculate the expected value. If the expected value is greater than zero, play the game. Otherwise, it would not be profitable.

Step-by-step explanation:

To determine whether or not you should play the game, we need to calculate the expected value. The expected value is the average amount that you can expect to win or lose per game. We can calculate it by multiplying the probability of each outcome by the amount won or lost for that outcome:

Probability of getting 3 or more doubles = 1 - Probability of getting 0, 1, or 2 doubles
Probability of getting 0, 1, or 2 doubles = (6/36)^5 + 5*(6/36)^4 * (30/36) + 10*(6/36)^3 * (30/36)^2
Probability of winning = 1 - Probability of losing
Probability of losing = Probability of getting 0, 1, or 2 doubles

Using these probabilities, we can calculate the expected value:

Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
Expected value = (1 * 30) - (Probability of losing * 1)

Since the cost per round is $1, the expected value should be positive in order to play the game. Therefore, if the expected value is greater than zero, you should play the game. Otherwise, it would not be profitable in the long run.