Question

A game is said to be fair if the expected value (after considering the cost) is 0. This would mean that in the long run, both the player and the "house" or whoever is putting on the game, would expect to win nothing. If the value is positive, the game is in your favor. If the value is negative, the game is not in your favor. At a carnival, you pay $1 to choose a card from a standard deck. If you choose a red card you double your money, but if you pick a black card you do not get any. (A standard deck of cards has 52 card. 26 of the cards are red.)

Answer 1

The expected value is 0

Game is fair

Explanation:

Probability = required outcome / Total possible outcomes

Number of red cards = 26

Numbw rof black cards = 26

Total number of cards = 52

If a red card is chosen, amount paid is doubled

If a black card is chosen, no winning or amount is collected.

Net money won or lost on choosing a red card = ($2 - $1) = $1

Net amount won on choosing a black card = $0 - $1 = - $1

P(red) = 26 /52 = 1/2

P(blue) = 26 /52 = 1/2

Expected value (E):

E = x*p(x)

E(X) = (1/2 * 1) + (1/2 * - 1)

E(X) = 1/2 - 1/2 = 0

Hence, since the expected value is 0 ; then the game is fair