SOLUTION: Suppose it cost $42 to roll a pair of dice. You get paid $6 times the sum of the numbers that appear on the dice. If the cost of the game is not taken into consideration, what is t

Question 838603: Suppose it cost $42 to roll a pair of dice. You get paid $6 times the sum of the numbers that appear on the dice. If the cost of the game is not taken into consideration, what is the expected value of the game? Is it a fair game?
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Look at the possible outcomes,
11=2
12=3
13=4
14=5
15=6
16=7
21=3
22=4
23=5
24=6
25=7
26=8
31=4
32=5
33=6
34=7
35=8
36=9
41=5
42=6
43=7
44=8
45=9
46=10
51=6
52=7
53=8
54=9
55=10
56=11
61=7
62=8
63=9
64=10
65=11
66=12
Calculate the probability for each sum,
Sum=2 or 12
Sum=3 or 11
Sum=4 or 10
Sum=5 or 9
Sum=6 or 8
Sum=7
The expected value is then,

Is it fair? The expected value equals the cost to play.

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Here are all the possible dice rolls: (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) Events Winnings X P(X) E(X)=X�P(X) ---------------------------------------------- rolling 2 2*$6=$12 1/36 $12/36 rolling 3 3*$6=$18 2/36 $36/36 rolling 4 4*$6=$24 3/36 $72/36 rolling 5 5*$6=$30 4/36 $120/36 rolling 6 6*$6=$36 5/36 $180/36 rolling 7 7*$6=$42 6/36 $252/36 rolling 8 8*$6=$48 5/36 $240/36 rolling 9 9*$6=$54 4/36 $216/36 rolling 10 10*$6=$60 3/36 $180/36 rolling 11 11*$6=$66 2/36 $132/36 rolling 12 12*$6=$72 1/36 $72/36 ------------------------------------------ Total expectation = ∑(E(X) = $1512/36 = $42

what is the expected value of the game?

$42

Is it a fair game?

Yes because the cost to play is $42, which is the same as the expectation. Thus if you play this game many times, you will average breaking even. (Games at fairs are NEVER fair. So no 'fair games' are fair games! hahaha!) Edwin

RELATED QUESTIONS
Suppose it costs $57 to roll a pair of dice. You get paid 8 dollars times the sum of... (answered by MathLover1,math_tutor2020)
Suppose it costs $48 to roll a pair of dice. You get paid $7 times the sum of the numbers (answered by ikleyn,greenestamps,robertb)
suppose it cost $8 to roll a pair of dice. we get paid the sum of the numbers in dollars... (answered by math_tutor2020,greenestamps)
Suppose it costs $15 to roll a pair of dice. You get paid 2 dollars times the sum of... (answered by ikleyn)
Suppose it costs $22 to roll a pair of dice. You get paid 3 dollars times the sum... (answered by stanbon)
Suppose it costs $5.00 to roll a pair of dice. If you get paid the positive difference... (answered by Edwin McCravy)
Suppose it costs $6.00 to roll a pair of dice. You get paid the large number in dollars... (answered by Boreal)
Suppose it costs $50 to roll a pair of dice. You get paid $7 times the sum of the numbers (answered by greenestamps)
Suppose you roll a pair of six-sided dice. (a) What is the probability that the sum of (answered by ikleyn)