**By: Nirisha Commodore**

**Probability**

What is Probability?

Probability Formula

The Probability Line

Types of Events

How likely something is to happen.

In mathematics, probability deals with calculating the likelihood of a given event's occurrence.

Example

When a single die is thrown, there are six possible outcomes: 1,2,3,4,5,6. The probability of any one of them is

1

/

6

.

Probability of an event happening

=

# of ways it can happen

_________________________

Total # of Outcomes

Probability is always between 0 and 1.

**Caution!**

**Probability is just a guide!**

Example:

If you toss a coin 100 times, how many heads will come up?

Probability says that heads have a 1/2 chance, so we might expect about 50 heads.

However, when we try it, we may get 48, 55, 5, or anything. Probability does not give us a definite answer.

Elements of Probability

Experiment/Trial

An action where the result is uncertain.

Sample Space

All possible outcomes of an experiment.

Sample Point

One of the possible outcomes.

Event

A single result of an experiment.

Independent

Dependent/

Conditional Probability

Event is not affected by another event.

Event can be affected by previous events.

Ex.

After taking one card from the deck, the probability of choosing another card changes.

Ex.

The amount of times a coin is tossed does not change the probability of the outcomes.

Tree Diagram

The tree diagram is used to picture dependent events.

Complement of an Event

All outcomes that are not an event.

Why is the complement of an event so important?

The complement is helpful in finding the probability of an event. If you know what it cannot be, it is easier to find what it can be.

Ex: Rolling a "5" or "6"

Event A: {5, 6}

Number of ways it can happen: 2

Total number of outcomes: 6

P(A) = 2/6 = 1/3

The Complement of Event A is {1, 2, 3, 4}

Number of ways it can happen: 4

Total number of outcomes: 6

P(A') = 4 /6 = 2/3

Let us add them: P(A) + P(A') = 1/3 + 2/3 = 3/3 = 1

Event A plus all outcomes that are not Event A make up all possible outcomes.

Relative Frequency

How often something happens divided by all outcomes.

Ex.

If the IEKHS football team won 2 games of a total of 12 played:

The frequency of winning = 2

The Relative Frequency of winning = 2/12 = 16.7%

Combinations and Permutations

In Mathematics:

If the order doesn't matter, it is a Combination.

If the order does matter it is a Permutation.

Combinations

There are 2 types:

Repetition is allowed (coins in your pocket)

No repetition (lottery tickets)

Permutations

There are 2 types:

Repetition is allowed

(a combination lock)

No repetition (the 1st

three people in a race.

1st,2nd, 3rd.

The factorial function (symbol: !) just means to multiply a series of descending natural numbers.

Ex:

4! = 4 × 3 × 2 × 1 = 24

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040

1! = 1

0! = 1.

Factorial Function

Probability theory is applied in everyday life in risk assessment and in trade on financial markets.

Application

Works Cited

www.mathisfun.com/data/probability.html

www.khanacademy.org/math/probability

www.mathgoodies.com/lessons/intro_probability

Life is all about taking chances!

If I invest in a house today, what are my chances in making a profit in the next 5 years?

Mutually Exclusive Events

It is impossible for two events to occur at the same time.

Ex.

Turning left and turning right.

P(A and B)= 0

(impossible)