In these lessons, we will learn how to find the probability of an event.

Related Topics:

Probability of Mutually Exclusive Events ("Or" events),

Probability of Independent Events ("And" events),

Probability of Dependent Events ("And" events without replacement),

Other Lessons on Probability

In an experiment,

The probability of an event *A*, written *P*(*A*), is defined as

**Example: **

When a fair dice is thrown, what is the probability of getting

a) the number 5

b) a number that is a multiple of 3

c) a number that is greater than 6

d) a number that is less than 7

* Solution: *

A **fair** die is an unbiased die where each of the six numbers is **equally likely** to turn up.

* S* = {1, 2, 3, 4, 5, 6}

a) Let *A* = event of getting the number 5 = {5}

Let n(*A*) = number of outcomes in event *A* = 1

n(*S*) = number of outcomes in *S* = 6

b) Let *B* = event of getting a multiple of 3

Multiple of 3 = {3, 6}

c) Let *C* = event of getting a number greater than 6

There is no number greater than 6 in the sample space *S.*

* C* ={}

A probability of **0** means the event will **never** occur.

d) Let *D* = event of getting a number less than 7

Numbers less than 7 = {1, 2, 3, 4, 5, 6}

A probability of **1** means the event will **always** occur.

**Example*** : *

Each of the letters HELLO is written on a card. A card is chosen at random from the bag. What is the probability of getting the letter ‘L’?

* Solution: *

Since the card is **randomly selected**, it means that each card has the same chance of being selected.

* S* = {H, E, L _{1}, L _{2}, O} There are two cards with the letter ‘L’

Let *A* = event of getting the letter ‘L’ = {L _{1}, L _{2}}

Example 1: Find the probability of the next person you meeting having a phone number that ends with 5?

Example 2: Find the probability of getting all heads if you flip 3 coins?

Example 3: Find the probability that the person that meet next has a birthday in February? (Non-leap year)

Example 1: What s the probability of drawing a spade from a deck of 52 playing cards?

Example 2: If a dart randomly hits the board below, what is the probability that it will hit the shaded region?

Example 3: It is Cindy's turn to spin in a game that she is playing with her friends. What is the probability that Cindy will have to move back on this spin?

Example: Suppose you spin the spinner below. Find the probability of spinning 4. Write the probability as a fraction, a decimal and a percent.

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