Posted by Brett on September 23, 2002 at 15:05:24:
In Reply to: Re: Drawing cards posted by Soroban on September 23, 2002 at 13:46:32:
: : Suppose you draw a card from a deck of cards. If the card is a club, you win three dollars. If the card is a spad or a heart, you win one dollar. If the card is a diamond, you must pay five dollars. Is this a fair game?
: You are evidently in a Finite Math course and don't understand any of
: the formulas or procedures ~ as evidenced by your three questions: percents,
: coin tosses, and expectation.
: It would help you showed us how far you got and/or ask specific questions
: about the problem. A mere "I'm really lost" just doesn't cut it.
: Most people will NOT "do" homework for you. There must be some Learning taking
: place. Otherwise, you'll be back tomorrow with the same problem (with "Hearts"
: changed to "Clubs").
: Are you familiar with a deck of standard cards? There are 52 cards, 13 of
: each of 4 suits. This means that the probability of getting a particular suit
: is 13/52 or 1/4.
: Let's say you play this game 40 times. What can you EXPECT to happen?
: 10 times you get a Club and win $3. Effect: +$30
: 20 times you get a Spade or Heart and win $1. Effect: +$20
: 10 times you get a Diamond and lose $5. Effect: -$50
: (Do you see where the "10" came from? 1/4 of 40 games?)
: What is the total Effect on your wallet?
: Think it out: you won $30 and $20, and lost $50. That's $0. (You break even.)
: Normally, we'd divide by the number of games at this point - to find your
: AVERAGE win or loss per game.
: But the question was "Is this a fair game?" and the answer is YES.
: (By defintion, a game with 0 expection is "fair".)
Thank you again Soroban. You provided a great explanation again.
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