SOLUTION: Isabel has a deck of 10 cards numbered 1 through 10. She is playing a game of chance. This game is this: Isabel chooses one card from the deck at random. She wins an amount of m

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Question 1190606: Isabel has a deck of 10 cards numbered 1 through 10. She is playing a game of chance.
This game is this: Isabel chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an even numbered card is drawn. She loses $5.50 if an odd numbered card is drawn.
A) Find the expected value of playing the game ($)
B) What can Isabel expect in the long run, after playing the game many times?
- Isabel can expect to gain money OR She can expect to win N dollars per draw.
- Isabel can expect to lose money OR she can expect to lose N dollars per draw.
- Isabel can expect to break even (neither gain nor lose money.)
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


On 10 draws with each card drawn once....

Winnings: 2+4+6+8+10=30
Losses: 5(5.50)=27.50

She gains an average of $2.50 in each group of 10 games, or $0.25 per game.

ANSWERS:
A) The expected value of playing is +0.25
B) She can expect in the long run to gain 0.25 dollars per draw.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
Isabel has a deck of 10 cards numbered 1 through 10. She is playing a game of chance.
This game is this: Isabel chooses one card from the deck at random.
She wins an amount of money equal to the value of the card if an even numbered card is drawn.
She loses $5.50 if an odd numbered card is drawn.
A) Find the expected value of playing the game ($)
B) What can Isabel expect in the long run, after playing the game many times?
- Isabel can expect to gain money OR She can expect to win N dollars per draw.
- Isabel can expect to lose money OR she can expect to lose N dollars per draw.
- Isabel can expect to break even (neither gain nor lose money.)
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(A)  the expected value playing the game = %281%2F10%29%2A%28%282%2B4%2B6%2B8%2B10%29+-+5%2A5.50%29 = 0.25 dollars.


     It means that she expects to win 0.25 dollars, in average, in each game, drawing a card.

Solved, answered and explained.