Question 321835: An urn contains 4 green, 6 blue and 10 yellow chips.
You pay $5 to draw a chip from the urn. Here are the rules of the game:
if you draw a green chip, the dealer returns you your bet and gives you an additional $5.
if you draw a blue chip, the dealer returns you your bet and gives you $1.
if you draw a yellow chip, the dealer keeps your $5.
What is the expected value of this game?
Tip: make a table with x-column money to win/lose (+/-) and probability column P(x)
that this happens, then calculate Expected Value of x E(x) for this distribution
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! urn contains 4 green, 6 blue, and 10 yellow chips.
Total number of chips is 20.
You pay $5.00 to bet.
Get a green chip and you get your money back plus $5.00.
Get a blue chip and you get your money back plus $1.00.
Draw a yellow chip and you lose your $5.00.
Probability of getting a green chip is 4/20.
Probability of getting a blue chip is 6/20.
Probability of getting a yellow chip is 10/20.
Your expected value will be calculated as follows:
4/20 * 5 = 20/20 = 1
6/20 * 1 = 6/20 = .3
10/20 * -5 = -50/20 = -2.5
Your Expected Value os 1 + .3 - 2.5 = -1.2
What this means is that, over the long term, you can expect to lose 1.2 dollars per game on average.
4/20 = 20% of the time you will win 5 dollar.
6/20 = 30% of the time you will win 1 dollar.
10/20 = 50% of the time you will lose 5 dollars.
If you played the game 100 times, you would win 5 dollars 20 times, win 1 dollar 30 times, lose 5 dollars 50 times.
Your total winnings would then be 20*5 + 30*1 - 50*5 = 100 + 30 - 250 which would equal a net loss of -120.
If you divide that by the number of games you played, you would 1.2 dollars per game on the average.
That's your expected value.
If you played the game 1000 times, then 200 times you get 5 and 300 times you get 1 and 500 times you lose 5.
200*5 + 300*1 - 500*5 = -1200.
Divide that by 1000 games and you averaged a loss of 1.2 dollars per game.
That's your expected value.
It's what you can expect per game on the average if you played that game over and over again for a large number of times.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! An urn contains 4 green, 6 blue and 10 yellow chips.
You pay $5 to draw a chip from the urn. Here are the rules of the game:
if you draw a green chip, the dealer returns you your bet and gives you an additional $5.
if you draw a blue chip, the dealer returns your bet and gives you $1.
if you draw a yellow chip, the dealer keeps your $5.
What is the expected value of this game?
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Gain for player:..............5......1......-5
Corresponding probability....4/20...6/20....10/20
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E(x) = [4*5 + 6*1 + 10*-5]/20 = [20+6-50]/20 = -24/20 = $1.20
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The Player can expect to lose $1.24 each time he plays the game.
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Cheers,
Stan H.
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