EXPECTATION “EXPECTED VALUE”. E XPECTATION – TELLS YOU THE AVERAGE AMOUNT OF MONEY YOU SHOULD EXPECT TO WIN OR LOSE IN A LOTTERY. PA Daily number: Play:

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Presentation transcript:

EXPECTATION “EXPECTED VALUE”

E XPECTATION – TELLS YOU THE AVERAGE AMOUNT OF MONEY YOU SHOULD EXPECT TO WIN OR LOSE IN A LOTTERY. PA Daily number: Play: $1 Payout: $500 If you play the daily number every day, what is the average amount of money you are losing per ticket?

S OLUTION : Set up a probability distribution where ‘x’ represents the amounts of money you can win or lose. Find the mean of the distribution: On average you would lose 50¢ per ticket. X = amount won or lost P(x) /10001/1000

G ENERAL I NTERPRETATION : If the mean is negative, then the game is in favor of the ‘house’. If the mean is positive, then the game is in favor of the player. If the mean is zero, then the game is fair.

E XAMPLE 2: A cash prize of $5000 is to be awarded by a fire department. If 2500 tickets are sold at $5 each, find the expected value of a ticket. The fire company is making $3 on every ticket. X = amount won or lost P(x) /25001/2500

E XAMPLE 3: A lottery offers one $2000 prize, two $500 prizes and five $50 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person buys one ticket. The lottery is making $1.75 on every ticket. X = amount won or lost P(x) /10001/10002/10005/1000