You are playing a card game. If you pull an Ace you win $26, if you pull the King of hearts you win $204, if you pull a jack or a queen you win $13, all other pulls you lose. What price should you be charged to make this a fair game? $5
$7
$6
$8

Using the expected value, it is found that a price of $6 should be charged to make it a fair game.

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The game is fair if the expected value is 0.The expected value is given by each outcome multiplied by it's probability.A probability is the number of desired outcomes divided by the number of total outcomes.In a standard deck, there are 52 cards.The cost of x.There are 4 Aces in a standard deck, thus probability of earning 26 - x.There is 1 King of Hearts in a standard deck, thus probability of earning 204 - x.There are 4 Jacks and 4 Queens in a standard deck, thus probability of winning 13 - x.The other 39 cards you lose, thus probability of losing x.

Considering we want the expected value to be 0.

$6 should be charged.

A similar problem is given at

The answer is 1532.75