warm up 1)if you pay $5 to play a game and you win $10, how much did you really win? 2)if there are...
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Warm Up1) If you pay $5 to play a game and
you win $10, how much did you really win?
2) If there are 4 numbers in a lottery drawing, how many numbers win? How many numbers lose?
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Expected ValueWhat can you expect to win over the long run?
Take the probability of each outcome and multiply by the “return”.
For example, tossing a coin.To play you pay $2.Heads prize is $5 and tails prize is 0.EV = .5(5-2) + .5(0-2) = .50
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The Definition
• Assume that an experiment has outcomes numbered 1 to n. with probabilities P1, P2…Pn.
• Each outcome has a value associated with it.• EV = P1V1 + P2 V2 + …+ PnVn
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When is a bet fair?
• When the expected value is negative, the player will lose money over the long run.
• When the expected value is positive, the player will win money over the long run.
• When is the bet fair for the player and the house?
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The BetRoll One Die
You pay $5 to play.1) If the roll is a six, the player wins $10.2) If the roll is 3,4 or 5, the player wins $5.3) If the roll is a 1 or 2, the player wins $0.Should you play?
EV = (P1)(V1) + (P2 )(V2) +(P3)(V3)
• Change the big payout until it is a fair bet.
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The Standardized Test• A student is taking a multiple choice test.• Each question has five possible choices.• For each correct answer, one point is awarded.• For each incorrect answer, 1/3 point is
deducted.• For a question with no response, no points are
awarded or deducted.• Is it wise to guess? EV = (P1)(V1) + (P2 )(V2)
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Redo with only 4 choices.EV = (P1)(V1) + (P2 )(V2)
Should you guess?
What happens when you only have three choices?EV = (P1)(V1) + (P2 )(V2)
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Using a tree for probabilitiesGiven the choices for an entre, side and desert, show a tree and state the probability. Entre: hamburger, chicken nuggets, or fish The probabilities were 40%, 45% & 15%. Side: French fries or coleslaw The probabilities were 80% & 20%.Desert: apple pie or ice cream The probabilities were 30% & 70%.
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Worksheet 7-5
Do #1 now.
Finish for homework.
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Using a chart for probabilities.Age / Hours
Less than 2
2 to 4
More than 4
Total
Children 20 10 2
Youth 15 25 10
Adults 5 20 10
Total Population
1) How many children were asked?2) How many watch 2 to 4 hours of TV?3) How many people were surveyed?4) What is the probability a) a child was asked? b) the person watched more than 4 hours of TV? c) given it was a youth, they watched less than 2 hours? d)given the person watched 2 to 4 hours, they were an adult?
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WS Practice 12-2
Do #1 now and finish the rest for homework.