a card game goes like this: you draw a card from a 52 card deck. If it is a face card jack queen or king you win 5 dollars; otherwise, you lose 2 dollars. What is your expected value for this game?
e(x)= (5)1/52-(2)1/52= 3/52 or 3.00
(5)(3/13) - 2(10/13) = -5/13
You better stay away from this game.
There are 13 cards in each suit of which 3, the jack, queen and king are winners. The other 10, ace through 10, are losers
To calculate the expected value for this card game, you need to multiply the value of each outcome by its probability and then sum them up.
In this game, there are 52 cards in the deck. The probability of drawing a face card (jack, queen, or king) is 12/52 because there are 12 face cards in a deck of 52 cards. The probability of not drawing a face card is 1 - 12/52 = 40/52.
The value of winning is $5, and the probability of winning is 12/52. So, the value of winning is (5)(12/52) = 60/52 = $1.15.
The value of losing is -$2, and the probability of losing is 40/52. So, the value of losing is (-2)(40/52) = -80/52 = -$1.54.
To calculate the expected value, you subtract the value of losing from the value of winning:
Expected Value = Value of Winning - Value of Losing
Expected Value = $1.15 - $1.54
Expected Value = -$0.39
Therefore, your expected value for this game is -$0.39. This means that, on average, you are expected to lose $0.39 per game.