Question

A card is drawn from a standard deck of 52 cards. If the card is a queen you get five dollars. If it is any other card, u lose one dollar.

1. Calculate the approximate expected value at this game. Round to the nearest cent.

2. Find the payout amount that would make this a fair game.

Answer 1

(1)

From the given data, the following Table iscalculated:

Event	Value (x)	Probability (p)	x.p
Card is a Queen	5	4/52 = 0.0769	5 X 0.0769 = 0.3846
Card is not a Queen	- 1	48/52 = 0.9231	- 1 X 0.9231 = - 0.9231
Expected value at this game.			0.3846 - 0.9231 = - 0.5385

So,

the approximate expected value at this game = - 0.54 (Loss)

(2)

Let

the payout amount = x.

So,

we get:

Event	Value (x)	Probability (p)	x.p
Card is a Queen	x	4/52 =1/13	x/13
Card is not a Queen	- 1	48/52 = 0.9231	- 1 X 0.9231 = - 0.9231
Expected value at this game.			x/13 - 0.9231

So,

the payout amount x that would make this a fair game. is given by:

So,

x = 13 X 0.9231 = 12.00

So,

Answer is:

12.00