Download Expected Value f09

$100
$100
90° 90°
60°
$200
60°
60°
$400
$300
1) If you spin once, what is the probability of getting each dollar
amount (fractions)?
1/2, 1/6, 1/6, 1/6
2) If you spin twice, what is the probability of getting $100 and then
$200?
1/12
3) If you spin twice, what is the probability of getting a sum of $600?
1/12
Benchmark #1-10
a)
2y
b)
4xy + 2y2
c)
4xy
d)
0
c
Benchmark #1-11
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?
b
a)
b)
c)
d)
Benchmark #1-12
Divide.
a)
b)
c)
d)
b
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?
Gain,x
$995 $495
Prob, p
1/2500
1/2500
$95
1/2500
-$5
2497/
2500
E = 995(1/2500) + 495(1/2500) + 95(1/2500) + (-5)(2497/2500)
= -$4.36
Homework
Page 357 #1-7 and Review for Quiz