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 4 numbers in a lottery drawing, how many numbers win?

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Presentation transcript:

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 4 numbers in a lottery drawing, how many numbers win? How many numbers lose?

Expected Value What 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

The Definition Assume that an experiment has outcomes numbered 1 to n. with probabilities P 1, P 2 …P n. Each outcome has a value associated with it. EV = P 1 V 1 + P 2 V 2 + …+ P n V n

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?

The Bet Roll 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 = (P 1 )(V 1 ) + (P 2 )(V 2 ) +(P 3 )(V 3 ) Change the big payout until it is a fair bet.

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 = (P 1 )(V 1 ) + (P 2 )(V 2 )

Redo with only 4 choices. EV = (P 1 )(V 1 ) + (P 2 )(V 2 ) Should you guess? What happens when you only have three choices? EV = (P 1 )(V 1 ) + (P 2 )(V 2 )

Using a tree for probabilities Given 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%.

Worksheet 7-5 Do #1 now. Finish for homework.

Using a chart for probabilities. Age / Hours Less than 2 2 to 4 More than 4 Total Children20102 Youth Adults52010 TotalPopulation 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?

WS Practice 12-2 Do #1 now and finish the rest for homework.