You are considering playing a card game. The rules of the game are such that you pick a card from a standard deck of 52 cards and if the card is a diamond, you win $30 . The catch is, you have to pay the dealer a fee of $10 to play the game

What is the expected value of this gamble? (Hint: In a standard deck of cards, ¼ of the cards are diamonds).

A deck of cards consists of 52 cards out of which, 13 are diamonds. Therefore in a random pick, the probability of picking a diamond is 13/52 = 1/4 . When a diamond is picked, the player wins $30, pays the dealer $10, and is left with $20 . The probability of not picking a diamond is 1 – 1/4, or 3/4 . When a diamond is not picked, the player win nothing, pays the dealer $10, and is left with -$10 . Therefore, the expected value of the gamble is (1/4 × $20) – (3/4 × $10) = -$2.50 . Since, the expected value of the gamble is -$2.50 a player loses an average of $2.50 each time he plays the game.