Agame is played by drawing a single card from a regular deck of playing cards. if you get a black card, you win
nothing. if you get a diamond, you win $5.00. if you get a heart, you win $10.00. how much would you be willing
to pay if the game is to be fair? explain.

Step-by-step 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:

answer: -2+√x,-2-√x

i hope this , i don't know if you're looking for a pair or not.

14

step-by-step explanation: