Warm-upUse the table to answer the questions.

1. What is the probability that someone wearing their seatbelt was going >15 mph over speed limit?

2. What is the probability that someone was going 10-15 mph OR was not wearing a seatbelt?

Number of mph over speed limit

10-15 >15 Total

Wearing Seatbelt

Yes 65 145 210

No 15 75 90

Total 80 220 300

Expected Value

• Essential Question - What is expected value used for in real-life?

What it is and what it is used for

• A weighted average• The expected results of an experiment in

the long run.• Used in business to predict future profits• Used in insurance to determine how much

a person’s insurance rate• Used in games such as the lottery, slot

machines, roulette to determine expected winnings (or losses)

How you find it

• Multiply each probability by amount you will win and then add all together

• Used in business to predict future profits• Used in insurance to determine how much

a person’s insurance rate• Used in games such as the lottery, slot

machines, roulette to determine expected winnings (or losses)

Example

• I will give you $1 if you roll an even number on a die and you give me $1 if you roll an odd number.

• Who would win money in the long run?• (prob of even)($1)+(prob of odd)(-$1)

• If the expected value is 0, the game is called FAIR

1 1($1) ( $1)

2 2

0

Interpreting Expected Value

• If you get a ZERO expected value, you expect to BREAK EVEN in the long run

• If you get a POSITIVE expected value, you expect to WIN in the long run

• If you get a NEGATIVE expected value, you expect to LOSE in the long run

• The value you get for expected value will probably NOT be one of the winnings of the game

Example 2

• If you roll a 1, I will give you $4 and if you don’t roll a 1, you give me $1.

• What is the expected value? Does this mean you will win or lose money?

• (prob of 1)($4) + (prob of NOT 1)(-$1)

• You will lose money over time

1 5($4) ( $1)

6 6

0.17

Example 3• Suppose it costs $5 to spin the spinner and you

win the amount you spin.

• What is your expected value? Should you play?• p(2)($2-$5)+p(10)($10-$5)+p(1)($1-$5)

• You should not play if you want to win money

1 1 1( 3) (5) ( 4)

4 4 2

1.50

Example 4You are taking a multiple choice test that has 4 possible

answers for each question.

You get 3 points for each correct answer and lose 1 point for each incorrect answer, and do not gain or lose any points for answers left blank.

If you do not know the answer to a question should you guess an answer to a question you don’t know?

Hint:1. Find the probability of each outcome.

2. Find the expected value of guessing the answer

Can we make money?At a roulette wheel there are 2 zeroes and 36 non zero

numbers (18 red and 18 black) to bet on. If I bet $1 on red what is the expected value of my bet?

How about after 10 of the same bets? How much can I be expected to win or lose?

Spinner

What is the expected value of the spinner?

$360018

$450 $1800 $800

$200

$500

$400

$700

$100

$300$600

Tables

x P3 .254 .30

13 .102 .35

Use your formula and calculate

(.25) 3 + (.30) 4 + (.10) 13 + (.35) 2 =

.75 + 1.20 + 1.30 + .70 = 3.95

Tables

Find the expected value of the following event.

1

173.8

30

6.85

x P

5 .25

8 .30

11 .10

6 .35

Classwork1. In a group with NO MORE than 4 people, you will calculate

the expected value of a single one dollar scratch off lottery ticket. Show the calculations you did to get the answer, even if you used a calculator.

2. If you purchased 1000 of these tickets, what would your net loss be?

3. Would it help your expected winnings if you and 9 other people bought a total of 100 tickets in the your lottery ticket game and split your earnings?  Why or why not?  (In other words, would you win more by pooling your resources with 9 others rather than buying only 10 tickets yourself?)

4. How does computing expected value of these tickets help a person to maintain a sensible perspective on purchasing lottery scratch game tickets?

Homework

pg. 357 #1-9

**Remember to check the ODDS in the back of the book!***