# Counting & Probability

## If you are here, you have to say goodbye to the good old days when counting was simply 1,2,3….

You are going to a supermarket when you realize that there are only 4 chocolate bars in a certain box. You decide to take two successively without replacing them, so you can enjoy them at home!

Basically the result is a number of two digits

What is the number of all possible outcomes?

Solution:

-Method 1: We apply the tree method that we all know since we were kids, but that would take too long!

-Best method: We can call it the Square Method: So basically we get:

4(it can be either 1,2,3,4)x3( has three because one was already used up)=12 possibilities

Lets say we take the SAME experiment, but know the chocolates are put back in place… because of guilt o:). We apply the Square method

4x4=16 Possibilities

## Factorial?

0!=1

1!=1

n!= n(n-1)(n-2)…..1

What is all of this?!

Example:

Tara,Basem,Hiba and Hadi have in english exam in turn.

Determine all possible turns for the four students.

4!= 4x3x2x1=24

When it comes to words and letters:

*Maths? 5! (having 5 letters)

*Lili, here we have repeated letters so saying 4! is considered wrong, so what we do is we divide the number of total letters in the word over the number of letters being repeated like this

(4!)/ (2!2!)

Harder Example:

3 boys and 2 girls want to sit down on a bench.

1)How many different ways can they sit?

5!——> 5x4x3x2x1=120 ways

2) Same question, but this time boys are next to each other as well as boys.

3!x2!x2=24 ## Some Vocabulary:

1) Universe set: The set of all possible outcomes

example: Ω={ 1,2,3,4,5,6……100}

2) Event: A set that is a subset in Ω

Example: S={2,3,4,5,6}

3) Elementary Event: {6}

4) Empty Set: ø

5) Cardinal of A: Card(A): number of all elements that are in A

Example: A{2,3}-Card(A)=2 The Probability Song