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.)
7
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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.)
7
10 9 K
3
a 7 δ
] 9 t K

Accepted Answer

The game is not fair. The expected value can be calculated as follows:

- Probability of choosing a red card: 26/52 = 1/2

- Probability of choosing a black card: 26/52 = 1/2

- Expected value = (1/2) * $2 (winning amount for red card) + (1/2) * $0 (losing amount for black card) - $1 (cost to play)

- Expected value = $1 - $1 = $0

Since the expected value is $0, the game is not in the player's favor, making it unfair.

Answer