Problema Solution
How much should be charged to play the following game so that it is "fair"? Suppose a person wins a $20 if a face card is drawn from a standard deck of cards. Otherwise, the person loses the amount they paid to play the game.
Answer provided by our tutors
Let 'x' be the money charged to play the game.
If the Expected Value equals 0 we call it a "fair" game.
We can compute the Expected Value by multiplying each outcome by the probability of that outcome, then adding up the products.
First outcome: $(20 - x) if a face card is drawn from a standard deck of cards
Probability of outcome: P("face" card is drawn) = (3*4)/(13*4) = 12/52 = 3/13
Second outcome: -$x if a card other than "face" cars is drawn
Probability of outcome: P("face" card is not drawn) = 1 - (3*4)/(13*4) =1 - 12/52 = 1 - 3/13 = 10/13
Expected Value = (20 - x)(3/13) - x(10/13)
(20 - x)(3/13) - x(10/13) = 0
by solving it we find
( click here to see the step by step solution
)
x = $4.615
the game will be "fair" if $4.615 is charged to play the game.