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Excel Skills Learned
Upon completing the sheet, you should have an understanding of:
1. Use the counting formulas =COMBIN(n,m) and =PERMUT(n, m)
Math Skills Learned
1. When to use permutations, P(n,m) or =PERMUT(n,m) and/or
combinations, C(n,m) or =COMBIN(n,m).
2. How to compute probabilities for events using counting.
3. How to convert probabilities into odds.
Instructions: Open the tab labeled “Games” and complete the
tasks indicated there. Start by entering your name where
indicated. Pay attention to the legend and note that the sheet is
self-checking.
Video on counting
This is a self grading sheet for columns B, D, F, and G. If your answer is correct it will
show green, else you will see red.
Game
35 horses ran in the Kentucky Derby. The Exacta bet involves picking the first two finishers in
order. Determine the number of outcomes for two horses finishing in the first two spots and
the probability of winning the Exacta bet if you pick the horses at random.
Enter your name in C2
Enter your name in C2
Enter your name in C2
Enter your name in C2
Enter your name in C2
Permutation
Combination
Your Name Here
Enter Name ⇒
Legend
If a cell is shaded
Salmon
You should
Make a selection
Blue
Green
Gold
Any other color
Enter a text response
Enter a number
Enter an Excel formula
Make no changes
Is this a permutation (the
Total # of outcomes for
order of picks matters) or a Describe how to calculate the #
the game (use
combination (the order
of outcomes
PERMUT() or
does not matter)?
COMBIN())
Permutation
Pick any 2 out of 35 horses,
where the order of selection
matters.
1190
Permutation
Combination
Describe how you can win this
game
Total # of ways that
you can win (enter a
number or formula as
indicated)
Probability of
Winning
Odds against
winning
= (1 – P)/P
You must pick the right first horse
and then the right second horse
1
0,0840336%
1189
Interpretation of odds.
Your odds of winning are 1 to 1189!
Your odds of winning are 1 to ???!
Your odds of winning are 1 to ???!
Your odds of winning are 1 to ???!
Your odds of winning are 1 to ???!
Your odds of winning are 1 to ???!
Guidance for Topic 6 DQ 2
1. As always, make sure to enter your name in C2.
2. Once you finish entering your name in C@, the questions that you have to answer appear
in column A.
3. Note that permutation takes into account the order of choosing while combination does not
consider the order. Their difference is explained in this web site:
https://www.mathsisfun.com/combinatorics/combinations-permutations.html
4. You have to be careful when your question involves the rule of product. It is explained
here: https://en.wikipedia.org/wiki/Rule_of_product
Example: Suppose there are 30 balls in total, and there are six correct balls. You pick up
four balls at the same time, and you win if you get two correct balls. Now, you have to
answer the total number of ways that you can win the game. First, you have to pick two
correct balls from six of them, and the number of ways that this occurs is =combin(6, 2).
At the same time, you have to pick two wrong balls from 24, and there are =combin(24, 2)
ways to choose the wrong balls. The rule of product states that, in total, there are =combin(6,
2)*combin(24, 2) ways to with the game.
Excel Skills Learned
Upon completing the sheet, you should have an understanding of:
1. More practice at using autofill.
Math Skills Learned
1. How to compute theoretical probabilities.
2. How to compute probabilities for events using counting.
3. How to compute empirical probabilities.
4. Investigate how the empirical probabilities and theoretical
probabilities are related to number of repetitions. (Central Limit
Theorem)
Instructions: Open the tab labeled “Probs” and complete the
tasks indicated there. Start by entering your name where
indicated. Pay attention to the legend and note that the sheet is
self-checking.
Your Name
Number of sides
13
Table 1 Number of Rolls
Table 2 Number of Rolls
The value in cells A7 and
A10 represent the
number of rolls in tables 1
and 2, respectively. This
value will serve as the
denominator when
calculating the empirical
probabilities in column F.
You should use a formula
here, for example, add up
all of the frequencies.
Roll
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Rolls for
Table 1
8
Rolls for
Table 2
12
this will rerun the sheet. How do the average deviations (from “The table
ge deviations”) compare between 1000 and 4000 rolls. What do you think would
f you rolled more often? What about less often?
Guidance for Topic 6 DQ 1
1. Drag down the formula in C4 until you hit roll 1,000. Do the same for D4, but this time,
you have to drag down the formula until roll 4,000.
2. Enter the total number of rolls in A7 and A10, which in this case is 1,000 for A7 and 4,000
for A10.
3. Enter a formula in H4 and drag down the formula in column H. Make sure to use $A$7 so
that your choice of A& is fixed.
4. Do the similar thing for I4. Make sure to use $A$4 so that your choice of A4 is fixed.
5. Use =average() in J19.
6. Repeat the procedure mentioned above for Table 2.
7. Type something and hit enter in the blue cells and you will get different numbers each time
for J19 and J38. Record these numbers in the table from rows 42 to 46. Alternatively, every
time you enter a number and hit enter in the green table, the numbers in J19 and J38 change.
Record these numbers.
8. Don’t forget to write your response in the blue space below the big arrow.
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