expectation word problem: determine if game is 'fair'

[MRS.FREE]

i can't figure out how to even set this up or where to start, please can someone help me????

A person pays $2 to play a certain game by rolling a single dice once. If a 1 or a 2 comes up, the person wins nothing. If a 3, 4, 5, or 6 comes up they win the differencr between the number rolled and the $2 to play the game. Find the expectation for this game? is this game fair?

I'm lost :-(

Thank You in advance!

 

[wjm11]

Re: HELP PLEASE! expectation word problem

A person pays $2 to play a certain game by rolling a single dice once. If a 1 or a 2 comes up, the person wins nothing. If a 3, 4, 5, or 6 comes up they win the differencr between the number rolled and the $2 to play the game. Find the expectation for this game? is this game fair?

Add the probabilities of winning money – and don’t forget to subtract the cost of playing!:

P(1 or 2) = 1/6 + 1/6 = 2/6 = 1/3
Multiply this probability times the amount of money won ($0):
(1/3)($0) = $0

P(3) = 1/6 times the amount won ($3 - $2 = $1):

(1/6)($1) = $.17

P(4) = 1/6 times the amount won ($4 - $2 = $2):

(1/6)($2) = $.33

P(5) = 1/6 times the amount won ($5 - $2 = $3):

(1/6)($3) = $.50

P(6) = 1/6 times the amount won ($6 - $2 = $4):

(1/6)($4) = $.67

Expected result is winnings minus cost of playing:

$1.67 - $2 = -$.33 (about a 33 cent loss for each play)

This is not a "fair" game.

 

[Denis]

Re: HELP PLEASE! expectation word problem

Dice:  1  2  3  4  5  6
Net : -2 -2 -1  0  1  2 = -2

Loses 2 bucks over 6 tosses, hence 2/6 = 1/3 = 33 1/3 cents per toss.

 

[MRS.FREE]

wow, thank you! once i see it i get it