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?

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

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

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 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.

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)

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)

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%.

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

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?

WS Practice 12-2

Do #1 now and finish the rest for homework.