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?
Answer: The equally likely outcomes of each roll are receiving $6, $5, $4, $3, $2, or $1. I think the answer is $3.50 since you are equally likely to win more or less than the cost. That is 3 of 6 possible outcomes are a gain for 50% chance of a gain, and 3 of 6 or 50% are a loss.
Is this answered correctly?
Thanks.
That's what I would say.
Thanks.
another way.
Expected value: 1/6 (6 + 5 + 4 + 3 + 2 +1)
= 1/6 (21)
The answer provided is close, but not entirely correct. To determine the fair cost of each roll, we need to consider the expected value.
The expected value of a random variable is calculated by multiplying each outcome by its corresponding probability, and then summing them up. In this case, the outcomes are the amounts of money you can win, and the probabilities are the chances of rolling each number on the die.
The probabilities for rolling each number on a fair die are all equal, since each of the six faces has an equal chance of being rolled. Therefore, each face has a probability of 1/6.
To calculate the expected value, we multiply each outcome by its probability and sum them up:
(1/6 * $1) + (1/6 * $2) + (1/6 * $3) + (1/6 * $4) + (1/6 * $5) + (1/6 * $6)
Simplifying this expression, we get:
($1 + $2 + $3 + $4 + $5 + $6) / 6
= ($21) / 6
= $3.50
So, the correct fair cost for each roll of the die in order for the game to be considered fair is $3.50.
Therefore, your answer of $3.50 is correct. Well done!