Download Expected Value

Expected Value
MM1D2 Students will use the basic laws of
probabilities.
d. Use expected value to predict outcomes.
Expected Value
• Expected value E of the collection of
outcomes is the sum of the products
of the events’ probabilities and their
values.
Expected Value
• The expected value or mean of a discrete
distribution is the long-run average of
occurrences. We must realize that any one
trial using a discrete random variable
yields only one outcome. However, if the
process is repeated long enough, the
average of the outcomes are most likely to
approach a long-run average, expected
value or mean value.
Spinner Game
Spinner Game
Spinner Game
Spinner Game
Spinner Game
Spinner Game
Try some…
• Consider a game in which two players
each choose an integer from 1 to 3.
If the sum of the two integers is
even, then player A scores 4 points
and player B loses 2 points. If the
sum is odd, then player B scores 4
points and player A loses 2 points.
Find the expected value for player A.
Answer
• The possible outcomes are
1+1
2+1
3+1
1+2
2+2
3+2
1+3
2+3
3+3
The probability of an even sum is 5/9. The
probability of an odd sum is 4/9.
Player A: E = 4(5/9) + (-2)(4/9) = 12/9 =4/3
Project
Create a spinner for a game.
Make sure you have at least seven sections
distributed into semicircles and cut angles.
Each spinner section needs to have numbers,
dollar amounts, etc.
Determine the expected value of 10 spins,
20 spins, and 50 spins.
Spinner Rubric
Group members:
3
Rubric
2
1
Construction
The spinner was neatly
constructed with evenly
distributed parts.
The spinner was
neat but did not
have evenly
distributed
numbers.
The spinner
was
constructed but
was not neat.
Reasoning
The problem was set up
correctly with
explanations given.
Formulas were used.
The problem was
set up correctly
with work shown.
No work
shown.
Delivery
All problems were
correct with well written
explanations.
Less than 2
mistakes.
2 or more
mistakes.
Scale:
9
8
7
100
95
90
6
5
4
3
85
80
75
70