Answer:
Explanation:
Previous concepts
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
Solution to the problem
For this case we need to use the definition of expected value given by:
For this case we need that the expected value would be 0 since we want a fair game.
Assuming a standard deck of 52 cards. We can find the probabilities for each possible event.
And we have the following values:
Let A the amount that we need to pay for a game we have this equality:
And if we solve for A we got: