You pick a card from a card deck of 52 cards. If you choose a diamond or a heart, you win $50. If you choose a club or a spade, you lose $60. Find the expected value of this game.
Prob(diamond or heart) = prob(club or spade) = 26/52 = 1/2
expected value = (1/2)$50 + (1/2)(-$60) = - $5.00
Weird ! , why would anybody play a game like that?
hahah thank you! good question because it sure wouldn't be me playing!
To find the expected value of the game, we need to calculate the probability of each outcome and multiply it by the corresponding outcome value.
First, let's determine the probabilities:
- There are a total of 52 cards in the deck.
- There are 13 diamonds and 13 hearts in the deck (total 26 cards), so the probability of choosing a diamond or a heart is 26/52 = 1/2.
- There are also 13 clubs and 13 spades in the deck (total of 26 cards), so the probability of choosing a club or a spade is also 26/52 = 1/2.
Next, let's assign the values:
- If you choose a diamond or a heart, you win $50.
- If you choose a club or a spade, you lose $60.
Now, we can calculate the expected value using the formula:
Expected Value = (Probability of Winning * Value of Winning) + (Probability of Losing * Value of Losing)
Expected Value = (1/2 * $50) + (1/2 * -$60)
Expected Value = $25 - $30
Expected Value = -$5
Therefore, the expected value of this game is -$5. On average, you would expect to lose $5 per game if you played many rounds.