1. U10D3 Have out: Bellwork: Work on the Probability Practice Worksheet.
Pencil, red pen, highlighter, GP notebook, textbook, calculator
U10D3
Have out:
Bellwork:
Work on the Probability Practice Worksheet.
Fill in the table with the sum of the two dice, then determine the probabilities.
total:

2. 1 2 3 4 5 6 7 8 9 10 11 12 1) P (sum > 7) = First Die+1
First Die 1 2 3 4 5 6 7 8 9 10 11 12 +1 +1
Second Die +1 +1

3. 1 2 3 4 5 6 7 8 9 10 11 12 6) P (at least 1 die is a 3) = First Die
7) P (both dice are a 3) =
8) P (4  sum < 6) =
9) P (sum > 10 or sum < 3) =
10) P (sum is odd) = +1
First Die 1 2 3 4 5 6 7 8 9 10 11 12 +1 +1
Second Die +1 +1
total:

4. Allowance Dilemma! For your allowance each week, you have 2 choices:
Take $12
or…
take your chance in the game of:
Allowance Dilemma!

5. $ 1 $ 20 $ 5 $ 1 $ 1 Here’s how it goes: Will you… A) Take $12 or…
B) Draw 2 bills, one at a time, replacing it each time, from a bag with three ones, one five, and one twenty dollar bill.
$ 1
$ 20
$ 5
$ 1
$ 1
What is your initial choice? (Circle one.) A or B
Eeny, meeny, miny, moe…

6. Let’s what happens when we chose option B
Let’s what happens when we chose option B. Record the observations on your worksheet.
Class trials:
1. _____
4. _____
7. _____
10. ____
13. ____
16. ____
2. _____
5. _____
8. _____
11. ____
14. ____
17. ____
3. _____
6. _____
9. _____
12. ____
15. ____
18. ____
Do you wish to alter your choice after the trials? __________
Yes No
What are the choices? or

7. The list of all possible outcomes is called the _____________.
sample space
For example, rolling 2 dice and finding the sum, the sample space is: S = {_________________________}
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
In the allowance dilemma problem, S = {________________}. 2, 6,
10,
21,
25, 40
Which outcome do you think is most likely? ____________
Make an educated guess.
Least likely? ____________

8. Let’s make an area model of the allowance dilemma
Let’s make an area model of the allowance dilemma. Determine all probability of all possible outcomes.
AREA MODEL
Fraction
Decimal
1ST BILL
P (____) = $2
= 0.36 $1 $1 $1 $5
$20 $1 2 2 2 6 21
P (____) = $6
= 0.24 $1 2 2 2 6 21
2ND BILL
P (____) =
$10
= 0.04 $1 2 2 2 6 21
P (____) =
$21
= 0.24 $5 6 6 6 10 25
$20 21 21 21 25 40
P (____) =
$25
= 0.08
P (____) =
$40
= 0.04

9. What total will you get if you add all the fractions?1
What total will you get if you add all the decimals? 1
Are all the outcomes equally likely to occur? No
Theoretically, which outcome will occur most often? $2
Least often?
$10
and
$40

10. Let’s make a tree model of the allowance dilemma using weighted branches.
probabilities
Since all branches are not equally likely, we put the ___________ on them.
But first, when you initially pull out a bill, what are the probabilities for:
P ($1) =
1ST BILL 
P ($5) = $1 $5
$20
P ($20) =
This is an example of a weighted tree diagram. If we had shown each possible outcome, we would have 5 branches. However, since the probability for $1 is the same for each dollar bill, we can make a weighted branch and thereby have a less “congested” tree.

11. Write the probabilities for the 2nd bill.
1ST BILL  $1 $5
$20
2ND BILL  $1 $5
$20 $1 $5
$20 $1 $5
$20 $2 $6
$21 $6
$10
$25
$21
$25
$40
Write the dollar total at the bottom of each pathway.

12. Does the 1st bill have any effect on the outcome of the 2nd bill? _____
INDEPENDENCE
NO!!!
Since the 1st bill and 2nd bill _______ affect each other, they are called ____________ events.
do not
independent
If A and B are ____________ events,
then P(A and B) = _____  _____. That is, we multiply the probabilities.
independent
P(A)
P(B)
Use this rule to find the probability of each pathway. (Verify it is the same as the area model.)

13. 1ST BILL  $1 $5
$20
2ND BILL  $1 $5
$20 $1 $5
$20 $1 $5
$20 $2 $6
$21 $6
$10
$25
$21
$25
$40
P ($2) =
P ($6) =

14. 1ST BILL  $1 $5
$20
2ND BILL  $1 $5
$20 $1 $5
$20 $1 $5
$20 $2 $6
$21 $6
$10
$25
$21
$25
$40
P ($10) =
P ($21) =

15. 1ST BILL  $1 $5
$20
2ND BILL  $1 $5
$20 $1 $5
$20 $1 $5
$20 $2 $6
$21 $6
$10
$25
$21
$25
$40
P ($25) =
P ($40) =

16. So… which is the best choice? A or B?
We know what to expect theoretically, but what would happen if we played the game many times?
What would be the long term average?
Let’s look at expected value.

17. EXPECTED VALUE
expect
is the amount we would _______ to win or lose each game on average if we played a game many times.
P($2)
P($6)
P($10)
E(game) = (_____)(___) + (_____)(___) + (_____)(____) + (_____)(____) + (_____)(____) + (_____)(____)
0.36 $2
0.24 $6
0.04
$10
0.24
$21
0.08
$25
0.04
$40
P($21)
P($25)
P($40)
$11.20
 This is not one of the outcomes in the sample space, S. It is the ________ average.
= _______
long run
Therefore, which is the best choice? A or B
Take the $12 and don’t look back.

18. Finish the assignment:
PM 30 – 34, 38, 39, worksheet