Probability of an Event and Independent Events

heartP

Probability of an Event

A measure of the likelihood that an event will occur.

Example: What is the probability of selecting a heart from a standard deck of cards?

Number of Desired Outcomesevent

Total Possibe OutcomesP

13

52

10.25 25%

4

Number of Hearts

Total Number of Cards

Independent Events

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.

When two events, A and B, are independent, the probability of both occurring is:  

and P A B P A P B

4 152 6 1

78

Ex: What is the probability of selecting an ace from a standard deck and rolling a 3 on a standard 6-sided die?

4312 Ace 3P P

Selecting a card does not affect rolling a die. They are independent events.

Example

Your teacher challenges you to a spinner game. You spin the two spinners with the probabilities listed below. The first letter should come from Spinner #1 and the second letter from Spinner #2. Find all of the possibilities and the probabilities of each possibility.

T

FI

A

U

12

16

13

P I

P U

P A

14

34

P T

P F

Example: Area Diagram

12

Spinner #1

Spi

nner

#2

IT UT AT

IF UF AF

13

16

14

34

18

112

124

38

14

18

I U A

T

F

124

:Example

P UT

Example: Tree Diagram

12

141

6

START

I

U

A

T

FT

FT

F

14

13

14

34

34

34

1 1 1

2 4 8

1 3 3

2 4 8

1 1 1

6 4 24

1 3 3 1

6 4 24 8

1 1 1

3 4 12

1 3 3 1

3 4 12 4

UT

124

:Example

P UT

1

24