**Alice in**

Wonderland

Wonderland

Alice was sitting on the riverbank, drowsily looking over her sister's shoulder at the book she was reading, when all of a sudden, she spotted a white rabbit in a waistcoat run past her. The rabbit pulls out his pocket watch, exclaims that he is very late, and pops down a rabbit hole.

Alice runs over to where she saw the rabbit disappear but she does not know which hole to choose because there are 4 holes! Little does she know, that 2 of the 4 holes lead her to where the rabbit went.

Alice follows the White Rabbit down the hole and comes upon a great hallway lined with doors. She finds a small key on the table but does not know which door it opens. There are 2

blue

doors, 3

red

doors, and 1

yellow

door.

Alice finally finds the correct door and opens it. Through it she can see a beautiful garden. Alice cries because the door is too small for her to pass through. She finds a bottle marked “DRINK ME” and downs the contents. She shrinks down to the right size to enter the door but cannot enter since she has left the key on the tabletop above her head. Alice discovers a cake marked “EAT ME” which causes her to grow to an inordinately large height.

Still unable to enter the garden, Alice begins to cry again, and her giant tears form a pool at her feet. As she cries, Alice shrinks and falls into the pool of tears. The pool of tears becomes a sea, and she swims to slowly makes it to shore where 9 animals stand on a bank. They are preparing for a race and Alice joins them.

10P3 = 10 x 9 x 8

= 720

Alice meets the White Rabbit again, who mistakes her for a servant and sends her off to fetch his things. While in the White Rabbit’s house, Alice drinks an unmarked bottle of liquid and grows to the size of the room. The white rabbit returns, fuming at the giant Alice. He throws rocks at her through the windows which turn into cakes.

The probability of Alice growing larger is 0.8, and the probability of her staying the same size is 0.5. Alice uses conditional probability to find out what the probability of her srinking after eating the mushroom is.

P(A|B)

P(AnB) = 0.5

P(B) = .8

Alice wanders through the forest and comes across a series of paths. There is a dark path and a light path, and off of each of those paths is a stone, sand, and gravel path.

Alice uses a tree diagram to figure out the amount of ways she can take the different paths.

dark path

light path

gravel path

stone path

sandy path

stone path

sandy path

gravel path

She meets a Caterpillar smoking a water pipe. Before the Caterpillar crawls away, he gives Alice 15 mushrooms and tells her that they can make her grow and shrink.

Out of the 15 that Alice was given, the Caterpillar said that 11 will make her grow and 5 of them will make her grow and shrink. Alice uses a Venn diagram to find out how many mushrooms will make her only shrink.

Grow

Shrink

Grow

and

Shrink

Alice was so distracted by how beautiful the mushroom was that she forgot what colours make her grow or shrink. She tastes a mushroom, and her neck stretches high above the trees!

Alice eats another mushroom and shrinks down to a normal height. She wanders until she comes across the house of the Duchess. She enters and finds the Duchess, as well as a grinning Cheshire Cat, and a Cook.

**Alice uses permutations to find out how many different ways she can shake hands with these three characters.**

The Duchess behaves rudely to Alice and then departs to prepare for a croquet game with the Queen.

Alice reenters the forest, where she meets the Cheshire Cat again. The Cat explains to Alice that everyone in Wonderland is mad, including Alice herself. Then, the Cheshire Cat gives directions to the March Hare’s house and fades away to nothing but a floating grin.

Alice travels to the March Hare’s house to find the March Hare, the Mad Hatter, and the Dormouse having tea together. She sits down with them.

Additive Counting Technique

Alice travels back to the house of the Duchess and joins the queen in a strange game of croquet. Alice needs to pick five players for her team. She can choose from the Cheshire Cat, the Cook, the Duchess, and 7 of the Queen's army of playing cards. Alice uses combinations to figure out how many ways she can pick a team of 5 players.

Alice wins the croquet match against the Queen of hearts. This makes the Queen very angry and she orders her army of playing cards to chase Alice. But Alice grew to a large size and was able to fight back at the army chasing her.

Therefore, Alice can try 6 different combinations of pathways.

S = 15

5

6

4

5 make Alice both grow and shrink

11 - 5 = 6

15 - 6 - 5 = 4

Check:

6 + 5 + 4 = 15

Therefore, 4 of Alice's mushrooms will cause her to shrink only

2

4

6!

2!3!

=

6 x 5 x 4 x 3 x 2 x 1

2 x 1 x 3 x 2 x 1

=

240

2

=

120

**Permutations**

Combinations

Sources

Sparknotes - Story Summary

http://www.sparknotes.com/lit/alice/summary.html

Storybook Pictures

Carroll, Lewis, and Emma Chichester Clark. Alice in Wonderland. Great Britain: HarperCollins Childrens Books, 2009. Web. 6 Oct. 2013.

The Queen's army is a standard deck of 52 playing cards . She defeats all of them but 2 aces and 3 jacks. Alice uses combinations to find to amount of ways she can knock over the 2 aces and 3 jacks.

Carroll, Lewis, and Deborah Hautzig. Alice in Wonderland. New York, New York: Penguin Group, 2010. 12-13. Web. 6 Oct. 2013.

**( )**

**4**

**2**

**( )**

**4**

**3**

**( )**

**44**

**0**

**= 6 x 4 x 1**

= 24

= 24

Therefore, Alice can knock over the 2 aces and 3 jacks 24 different ways.

=

P(AnB)

P(B)

Suddenly, Alice wakes up underneath the tree, beside her sister. "What a strange dream." says Alice.

"I'd love to hear about it." says her sister.

Alice closed her eyes and started to tell her sister about all the wonderful things in her dream, the White Rabbit, the Mad Hatter, the Army of playing cards and all the other creatures she met.

=

0.5

0.8

= 0.625

**3! = 3 x 2 x 1**

= 6

= 6

(dark path, stone path)

(dark path, sandy path)

(dark path, gravel path)

(light path, stone path)

(light path, sandy path)

(light path, gravel path)

Therefore, there are 6 ways that Alice can shake the hands of the Duchess, the Cheshire Cat and the Cook.

# correct holes that Alice can choose

total # of holes

=

=

1

2

10 x 9 x 8 x 7 x 6

5!

**=**

**=**

**252**

Therefore, there are 252 ways that Alice can pick a team of 5 players from the Cheshire Cat, the Cook, the Duchess and 7 of the Queens playing cards.

= (1 x 3) + (1 x 3) + (1 x 3)

= 3 + 3 + 3

= 9

Therefore, there are 9 different ways Alice can choose from 3 kinds of tea and have 1, 2 or 3 spoonfuls of sugar.

The probability of Alice growing from the mushroom is 51%. Alice uses Odds to find out the odds of her growing versus shrinking.

P(growing) = 0.51

= 51

= 51:49

100

100 - 51= 49

Therefore, the odds of Alice growing versus shrinking is 51:49

=

(Multiplicative Counting Principle)

(Permutations with Indistinguishable Objects)

(Permutations)

Conditional Probability

Principle of Inclusion/Exclusion

**Combinations**

Maddy and Kaitlyn

Out of three different kinds of tea, Alice can pick one. She may also choose to have one, two or three spoonfuls of sugar. Alice uses the Additive counting technique to find out the number of ways she can have her tea.

Alice uses the multiplication counting principle to figure out her chances of picking the right hole.

Alice needs to know which door matches the key she found. She uses permutations with indistinguishable objects to find out how many ways she can try unlocking the doors.

There are 9 animals plus Alice in the race. Alice really wants to get either first, second, or third place in the race. To find out what her chances are, Alice uses permutations.

**Odds**

**=**

Therefore, Alice has a 1 in 2 chance of picking the correct hole.

Therefore, Alice can try unlocking the doors in 120 different ways.

Therefore, there are 720 ways that first, second and third can be awarded.

Therefore, Alice has a 63% chance that the cake will make her small again.