Posted by Soroban on September 23, 2002 at 13:46:32:
In Reply to: Drawing cards posted by Brett on September 23, 2002 at 11:38:09:
: 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?
Brett,
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".)