1. Warm-up
$100
$100
90°
90°
60°
60°
$200
60°
$400
$300
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?
1/2, 1/6, 1/6, 1/6
1/12
1/12

2. When do you find the expected value of an experiment?
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.

3. 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 + p3x pnxn

4. Example 1 Find the expected value.
.20 2
.30 3
.10 4
.40
E = 1(.20) + 2(.30) + 3(.10) + 4(.40) = 2.7
If I do this experiment 10 times, what total value would you expect to get?

5. Example2 Find the expected value. Gain, x 10 15 20 30 Probability 0.20
0.30
E = 10(.20) + 15(.30) + 20(.30) + 30(.20) = 18.5
If I do this experiment 10 times, what total value would you expect to get?

6. Example 3
You take an exam that has 5 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)(1/5) + (-1)(4/5) = -1/5

7. E = 995(1/2500) + 495(1/2500) + 95(1/2500) + (-5)(2497/2500)
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
$95
-$5
Prob, p
1/2500
2497/
2500
E = 995(1/2500) + 495(1/2500) + 95(1/2500) + (-5)(2497/2500)
= -$4.36

8. Example 5
You have a box with two nickels, one dime, three quarters, and two half dollars. Find the expected value of removing one coin.
Make a table of values and probabilities:
Calculate the expected value:
5(0.25) + 10(0.125) + 25(0.375) + 50(0.25) =
cents
Value 5 10 25 50
Probability
1/4
1/8
3/8

9. Homework
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We will spend the rest of class doing the spinner task.
Quiz tomorrow (Wednesday)
Review Thursday
Test Friday

10. Test Review Ch 3 Counting and Probability Practice
16 – 19, 24,
Chapter 3 Test Review
12 – 29 all