1/2, 1/6, 1/6, 1/61) If you spin once, what is the probability of getting each dollar

amount (fractions)?

2) If you spin twice, what is the probability of getting $100 and then $200?

3) If you spin twice, what is the probability of getting a sum of $600?

1/12

$100 $100

$200

$300

$40060°

60°60°

90° 90°

1/12

Benchmark #1-10

a) 2y

b) 4xy + 2y2

c) 4xy

d) 0

c

Benchmark #1-11

a) b)

c) d)

b

At Masterson Department Store, they issue prices for their clothing using polynomials and the variable x. The following is a sample listing of their prices.

If Heather wants to buy three pairs of pants, one pair of shoes, and two dresses, how much will her total bill be?            

Benchmark #1-12

a) b)

c) d) b

Divide.            

Math I

UNIT QUESTION: How do you use probability to make plans and predict for the future?Standard: MM1D1-3

Today’s Question:When do you find the expected value of an experiment?Standard: MM1D2.d.

6.5 Expected Value

A collection of outcomes is partitioned into n events, no two of which have any outcomes in common. The probabilities of the n events occurring are p1, p2, p3,..., pn where p1 + p2 + p3 + pn = 1. The values of the n events are x1, x2, x3,..., xn.

E = p1x1 + p2x2 + p3x3 + ... + pnxn

Example 1

• A person is rolling a die. They will be paid the dollar value equal to the number of dots on the die (i.e. roll a 6, make $6). What would be the expected value of a single roll?

E = 1/6(1) + 1/6(2) + 1/6(3) + 1/6(4) + 1/6(5) + 1/6(6)

=21/6 = $3.50

Example 2

Find the expected value.

E P(E)

1 .20

2 .30

3 .10

4 .40

E = 1(.20) + 2(.30) + 3(.10) + 4(.40) = 2.7

Example 3

You take an exam that has 4 possible answers for each question. You gain 3 points for each correct answer, lose 1 point for each incorrect answer, and do not gain or lose points for blank answers. If you do not know the answer to a question is it to your advantage to guess the answer?

E = (3)(1/4) + (-1)(3/4) = 0

Example 4

At a raffle, 2500 tickets are sold at $5 each for 3 prizes of $1000, $500, and $100. You buy one ticket. What is the expected value of your gain?

E = 995(1/2500) + 495(1/2500) + 95(1/2500) + (-5)(2497/2500)

= -$4.36

Gain,x $995 $495 $95 -$5

Prob, p 1/2500 1/2500 1/2500 2497/

2500

Homework

Page 357 #1-7 and Review for Quiz