Transcript Slide 1

Cinderella
Once upon a time, there lived a young girl
named Cinderella. She lived with her evil step-mother
and two evil step sisters. Her sisters always got what
they wanted, but only because of Cinderella. Cinderella
is like their personal maid. She cooks, she cleans, and she
does their laundry. She’s only allowed to do what she’s
told to do. With the help of her only true friends, the
mice and the birds, Cinderella’s dreams would come true
with the wish that her heart would make. The great
thing about Cinderella is no matter what, she’s always
happy and finds some way to put a smile on even
though she’s working constantly.
Cinderella
One day Cinderella was getting ready for the day, when Jaq found a mouse
in the mouse trap that Cinderella’s Step-mother had put out. Jaq quickly ran to
Cinderella and explained to her who he had found. Cinderella quickly followed Jaq
towards the trap to help this poor mouse. Of course, the new mouse was extremely
frightened, but Jaq quick to calm him down, so that Cinderella could comfort him. Like
all the other mice, the new mouse needed to be dressed. Luckily Cinderella had 5 shirts
and 5 hats for the new mouse to choose from. How many COMBINATIONS of 2 can
Cinderella make?
Total amount of clothing = 10
10
  = 45
2 
Therefore, the total amount
of outfits that Cinderella
can choose is 45.
Cinderella
Cinderella’s first chore of the day was to make sure that all the animals
got fed. So first she went and woke up Lucifer and brought him to the kitchen,
where Bruno was still fast asleep. After she fed the animals the mice came down
to pick up the leftovers, but soon realized that they would need to get past
Lucifer first. With Jaq being the distraction, the other mice were able to grab
some food. Unfortunately, on the way back to the kitchen, the new mouse, Gus
Gus, grabbed to much food and ended up spilling them all over the floor, which
caught Lucifer eye. Scared to death, Gus Gus ran up the table and hid underneath
a tea cup. Lucifer used THEORETICAL PROBABILTLY to figure out which
cup Gus Gus was under.
P(Picking the right tea cup) = 1/3
Cinderella
Meanwhile, back at the
palace, the King discusses with the
Duke about the arrangements for his son
to get married. The only problem is, the
King is unsure that his son will find a
suitable young lady on his own. The
only way his son would agree to this
ball was if the King could figure out
how many ways the quartet of singers
could be arranged in a row on the stage.
So the King and the Duke together used
the FUNDAMENTAL PRINCIPLE
OF COUNTING to find the answer.
4 x 3 x 2 x 1 = 24 Different ways
Therefore, there are 24 different
ways that a quartet of singers could
be arranged at the ball.
They will plan to invite all the eligible
bachelorettes in the kingdom. So they make up a
letter to send to the ladies, in hopes of their
arrival for the evening. When the Prince hears
about the ball for his arranged marriage, he’s not
impressed. Although the Prince would love
to find his Princess, he does not feel
comfortable with the idea that the ball is his
last opportunity to find the girl of his
dreams. Little did he know that not only
would he fall in love but he would also find
his Princess.
Cinderella
While Cinderella worked as hard as she could, there came a knock at the door.
Cinderella and her step-sisters had gotten invited to the ball to meet the prince, and he was
to choose his princess there. The step-sisters ran around getting their dresses ready, and
choosing what to wear, and then Cinderella asked if she could go. Her step-mother decided
to agree only if she was finished all her chores in time and was able to find something
suitable to wear. Cinderella was so excited she ran up the stairs and started to make her
dress out of whatever she could find, but then she heard her step-mother and sisters
yelling, “Cinderella! Do my laundry” “Cinderella! Where are my beads?” “Cinderella! Wash
the dishes!” Then Cinderella’s hopes and dreams of going to the ball were destroyed because
of all the chores she had to do. So Cinderella just
did as she was told and tried to finish them as
fast as she could. Meanwhile, Cinderella’s
friends decided they wanted to help her finish
her dress. So they all came together and started
to make Cinderella’s dress.
Cinderella
So all the birds and mice came together and decided on who was helping
with what. There were seven SUBSETS of jobs. If there was 7 birds measuring, 9
male mice cutting, and 12 female mice are sewing, while 3 are measuring and cutting,
5 are measuring and sewing, 4 are sewing and cutting, and 2 are doing all three.
How many females are actually just sewing?
Since there are 12 female mice sewing,
adding up the numbers in the middle of
U
the circles(3,2 and 2), the outcome will be
7. So if you take 12 and subtract 7, the
answer will be 5. So therefore, the
OUTCOME is 5 female mice just sewing.
Cinderella
After everyone had started making the dress, Gus Gus wanted to know the
probability of him helping out with his favourite jobs; sewing and cutting.
So Gus Gus used ADDITIVE COUNTING PRINICPLE to figure it out. These are
NON-MUTUALLY EXCLUSIVE EVENTS.
P(SUC)= P(S)+P(C)-P(SnC)
P(SUC)= 5/21 + 4/21- 4/21
P(SUC)= 5/21
Cinderella
After everyone worked so hard to finish Cinderella’s dress, they decided to
surprise her and show her what they had created. Cinderella was so excited and put the
dress on as fast as she could, and ran down the stairs. As soon as her Step-sisters and
Step-mother saw her theirs jaws dropped, and they found every reason to tare her dress
apart, grabbing their beads from her neck, ripping ribbon off the her dress, and then
Cinderella’s dress was destroyed.
She ran outside and starting crying harder then she had ever cried before, but
while Cinderella was crying, her fairy godmother came and rescued her. This is a
DEPENDENT EVENT because the only way that Cinderella can go to the ball now is
if her fairy godmother comes and makes her dreams come true.
Cinderella
“Don't cry, child," said a gentle voice. "I am your fairy godmother, and
I have come to help you." Then the fairy godmother waved her wand. Four mice
became four proud horses, and a big, round pumpkin became a glittering coach.
Again the fairy godmother waved her wand and turned Cinderella's torn dress
into a beautiful gown. "You must leave the ball by midnight," she warned.
"After that, the magic spell will be broken." When Cinderella first got to the
ball, she only knew 21 of the girls (Set A). The rest of the girls she did not
recognize (Set B). The total amount of girls that attended the ball was 126
(n(AUB) . This is a MUTUALLY EXCLUSIVE event. At the ball, the Prince
danced with Cinderella all evening. She felt as if she were floating on a dream!
n(AUB) = n(A) + n(B)
126= 21 + n(B)
126-21=n(B)
n(B)= 105
Therefore, Cinderella
doesn’t know 105 young
ladies at the ball.
Cinderella
The King and the Grand Duke were delighted to see them falling in love. But
as the clock struck midnight, Cinderella ran from the palace. She was in such a hurry that
she left one glass slipper behind. The Prince ran after her, but it was too late. The next
day, the Prince sent the Grand Duke door-to-door to find the young woman who had lost
her slipper. The Grand Duke had 10 girls try on the glass slipper before Cinderella even
got to try it on. The slipper either fit or did not fit. Using EXPERIMENTAL
PROBABILITY, the Grand Duke found out the probability of the slipper fitting the
other girls. When they got to Cinderella's house, both stepsisters tried on the glass slipper,
but their feet were much too big.
Cinderella
The EVENT, or the possible outcome of
the experiment, is two.
Outcome A occurs if the glass slipper
doesn’t fit any of the other girls.
Outcome B occurs if the glass slipper fits
the other girls.
The TRIAL is a reappearance of the
experiment. There were 10 trials for the
slipper.
Trial
Outcome
A
Outcome
B
1
x
2
x
3
x
4
x
5
x
6
x
7
x
8
x
9
x
10
x
The probability of the glass slipper not
fitting the other girls is 9/10 or 90%
Cinderella
Cinderella's stepmother told the Grand
Duke that there were no other ladies in the
house. She had locked Cinderella in her room
upstairs on purpose. Her step-mother put the key
in a box and locked it away. In order for her
friends to get the key from the box, Jaq and Gus
Gus needed to solve a problem to unlock the box.
The problem was (a+b) 7 and they
needed to find the third term. Gus Gus and Jaq
automatically started using PASCAL’S
TRIANGLE to solve the problem.
Row 0: :
1
Row 1:
1 1
 7  = a5b2
 
Row 2:
121
which
2


Row 3: 1 3 3 1
equals
Row 4: 1 4 6 4 1
21 a5b2
Therefore, the answer to open up the box is
21 a5b2.
Gus Gus and Jaq grabbed the
key, opened the door and freed Cinderella
just in time! When Cinderella appeared
and asked if she could try on the slipper,
her stepmother was furious. She tripped
the footman who was holding the slipper
on a pillow.
Cinderella
What’s the CONDITIONAL
PROBABILITLY that Cinderella pulls
out a glass slipper, given that there is
only one glass slipper left, since the
other one shattered?
P(C | GS) = P(C | GS)
P(GS)
=½ =½x2
½
= 1
Therefore the probability that Cinderella
has the other glass slipper is 1.
It fell to the floor and shattered.
But Cinderella reached into her apron
pocket and pulled out the matching one. It
was a perfect fit!
Cinderella
As Cinderella was running down the stairs to try on the shoe, the Grand
Duke decided the only way Cinderella could try on the glass slipper was to figure
out this PERMUTATION. In how many ways can the letters of the word
CINDERELLA be arranged if the ‘word’ must begin with L and end with a
vowel?
CINDERELLA
2 87654321 4
8!
= 2 x 8! x 4
= 322560
Cinderella
The Grand Duke was happy and relieved
that he had found the slipper's owner, he told the
Princess how beautiful she looked and this was a
COMPLEMENT ;) . The Prince would be
married at last. And Cinderella's dreams would all
come true.
THE END