EXPECTATION“EXPECTED VALUE”

EXPECTATION – 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?

SOLUTION: 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)

-1 499999/1000 1/1000

999 11 4991000 1000

.50

GENERAL INTERPRETATION: 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.

EXAMPLE 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)

-5 49952499/250

01/2500

2499 15 49952500 2500

3

EXAMPLE 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)

-5 1995 495 45992/10

001/1000 2/1000 5/1000

992 1 2 55 1995 495 451000 1000 1000 1000

1.75