The game of dots is played by rolling a fair die and receiving $1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?
The expected value of throwing the die is..
1/6(1+2+3+4+5+6)=21/6 dollars. That is the fair cost of playing the game.
To determine the fair cost for each roll in the game of dots, we need to examine the expected value. The expected value represents the long-term average value of an event occurring and is calculated by multiplying each possible outcome by its probability and summing the results.
In this game, the number of dots showing on the top face of the die ranges from 1 to 6, each with an equal probability of 1/6 because it is a fair die. So, the expected value (EV) for each roll can be calculated as follows:
EV = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6)
= (1 + 2 + 3 + 4 + 5 + 6) / 6
= 21 / 6
= 3.5
The expected value of each roll is 3.5 dollars. For the game to be considered fair, the cost for each roll should be equal to the expected value. Therefore, the fair cost for each roll in this game of dots would be $3.50.