Data Story Book

By Sarah Doyle
Emperor Kuzco was a selfish teenage emperor in a land far far away. He had hundreds of servants to
wait on him hand and foot, his own comfy throne and a giant palace. Yet, Kuzco still wasn’t happy. He
wanted to build himself an enormous summer home called Kuzcotopia, complete with a swimming pool
to lounge in all day long. He knew he would have to demolish one of the villager’s houses in order to do
so, but there was one location he wanted in particular: right on top of the tallest hill in the village. This is
Pacha’s house; a kind villager with a heart of gold, a loving wife, young two children and another on the
way. There are 100 households in the village, 75 of them belonging to families, but Kuzco wants
Patcha’s. Kuzco uses his knowledge of THEORETICAL PROBABILITY to figure out the probability
that out of all of the houses in the village, the house on the top of the hill would belong to a family.
P(The House Belonging to a Family) = 75/100 or 3/4
Yzma, Kuzco’s assistant, is jealous of Kuzco’s power and wants to get rid of him so that she
can take over the empire and make it “Yzmopolis”. So, she and her dopey assistant named
Kronk decide to go to their secret lair to brainstorm an evil plot. In order to get to the secret
lair, they have to pull the lever and correctly enter a 5-character combination in order to be
admitted access. They already remember the first and last two terms, but can’t remember the
third. The equation of the third term is (a+b) . Kronk and Yzma know that
5 the best way to find
the third term is to use PASCAL’S TRIANGLE.
Row 0:
Row 1:
Row 2:
Row 3:
Row 4:
Row 5:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Yzma and Kronk know that the third term in the fifth row is
10 (5C2), so the third term must have a coefficient of 10. Yzma reminded Kronk that
the exponents of “a” decrease by one each time as follows:
a 5+ a 4+ a 3
1
2
3
Since they know that the exponents of the terms “a” and “b” must equal five, “b”
must have an exponent of two (3+2=5). Therefore:
The Third Term of the combination =
3 2
10a b
Now it’s time to find the perfect potion to get rid of Kuzco once and for all!
Yzma wants to turn Kuzco into an animal so that he can no longer be
emperor, but what? There are a total of seven SUBSETS of animal potions:
22 furry animals
27 household pets
18 mammals
5 furry mammals
8 household mammals
9 furry household pets
3 animals who are all three
Let “F” represent furry animals, “H” represent household
pets and “M” represent mammals.
F
11
2
6
3
8
M
H
13
5
Therefore, there are 48 different
potions that Kronk and Yzma
could use on Kuzco. Yzma
decides that she wants to turn
him into an animal that is both
furry and a mammal. These are
NON-MUTUALLY
EXCLUSIVE EVENTS
because an animal can be both
furry and a mammal.
Let “O” represent an orange
chalice and “Y” represent yellow.
U
Now it’s time to have Kuzco over for
dinner to drink the potion. Yzma is
waiting in the dining room with Kuzco
and Kronk can’t remember which cup
has the poison in it. There are 30
chalices in total.
5 are purple
6 are red
6 are red and purple
7 are yellow
4 are orange
2 are yellow and orange
Kronk knows for a fact that the poison
is in either a yellow or a orange cup; he
just can’t remember which. To find the
probability of him choosing either a
yellow or an orange chalice, Kronk
uses the ADDITIVE COUNTING
PRINCIPLE.
P(OUY)=P(O)+P(Y) - P(O Y)
P(OUY)=4/30 + 7/30 - 2/30
P(OUY)=9/30
Therefore, there is a 9/30 or 30%
chance that Kronk chooses an
orange or yellow cup.
Lucky for Kronk, it worked! Kuzco transforms into a llama before their very
eyes and Kronk knocks him out with a dinner plate. Now only to hide the body.
Kronk stuffs Kuzco into a sack and goes to get rid of it. Of course, leave it to
Kronk to drop it down the hill, only to land on one of the villager’s carts. The
only problem is, there are hundreds of identical carts in the market and Kronk
can’t locate Kuzco. Hopefully this doesn’t come back to bite Kronk.
Later on, Patcha is unloading his cart when
he hears a moan. He opens his sack only to
find a llama! Patcha screams, but Kuzco
assures him that he’s the emperor and needs
to find his way back to the palace. They make
a deal that if Patcha helps Kuzco navigate the
way home, Kuzco will choose to build his
summer home somewhere else.
This is a DEPENDENT EVENT because Patcha’s home being saved is
dependent on whether or not they find their way back and if Kuzco stays true
to his promise. The probability of Patcha keeping up his end of the promise is
1/2, and the probability of Kuzco doing the same is 1/4.
P(Both Promises are Kept)=1/2 x 1/4
P(Both Promises are Kept)=1/8 or 13%
Therefore, there is a 13% chance that both Patcha
and Kuzco will be satisfied by this deal.
Meanwhile, Yzma finds out that Kuzco is still alive and on the lose in one
of the six nearby villages. Yzma and Kronk choose to roll a six-sided die six
times in order to decide which village they should search first.
The SAMPLE SPACE is S={1, 2, 3, 4, 5, 6}
Let 1 represent the village that Kuzco is in, and 2, 3, 4, 5 and 6 represent
the other villages respectively.
Roll #
Number on Die
1
4
2
2
3
1
4
6
5
3
6
2
The outcome of the die roll shows that
they have a 1/6 chance of choosing the
correct village to search first.
Yzma and Kronk finished their die roll but are still split on their decision.
Yzma says that they should go to village two because it was rolled the most
times, but Kronk says that his gut is telling him to search village one. So,
they decide to toss a coin three times, and the person to win two or more
times gets to search their choice of village first. Kronk chooses tails and
Yzma chooses heads. Let H represent heads and T represent tails.
All of the possible outcomes are as follows:
H
T
H
H
T
T
H
H
T
H
T
T H
T
Since Kronk’s gut is right and Kuzco is indeed in village one, there is a 4/8 or
1/2 (50%) chance that Kronk wins and they search the correct village first.
All of this searching for Kuzco sure works up an appetite! Kronk and Yzma
decide to stop at a diner in the nearest village for a bite to eat. There are 20
different options on the menu. 10 are regular food items, and 10 are the same
food items but made to be gluten free. The evil duo are extra hungry and
decide to order one meal each plus a third to share, but Yzma despises gluten
free food. The total amount of COMBINATIONS of entrees they can have if
two of the options have to be non-gluten free are as follows:
( ( x ( ( = 450
10
2
10
1
Therefore, there are a total of 450 combinations of food platters that Kronk
and Yzma can order.
Meanwhile, Patcha and Kuzco find their way back to the palace. They discover
the antidote in Yzma’s secret lair and Kuzco transforms back into a human. He
decides to stay true to his word and cancel the demolition of Patcha’s home.
Who knew the emperor being turned into a llama was all he needed to be freed
from his selfish ways?
As for Kronk and Yzma? Well, some things never change.
KROOOOOOOOOOOOONK!
The End