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12.5

Probability of Independent and

Dependent Events

GOAL

1

P

I

E

ROBABILITIES OF

NDEPENDENT

VENTS

What

you should learn

GOAL

Find the probability

1

Two events are

if the occurrence of one has no effect on the

independent

of independent events.

occurrence of the other. For instance, if a coin is tossed twice, the outcome of the

first toss (heads or tails) has no effect on the outcome of the second toss.

Find the probability

GOAL

2

of dependent events, as

applied in Ex. 33.

P R O BA B I L I T Y O F I N D E P E N D E N T E V E N T S

Why

you should learn it

If A and B are independent events, then the probability that both A and B occur

To solve real-life

is P(A and B) = P(A) • P(B).

problems, such as finding

the probability that the

Florida Marlins win three

games in a row in

Probability of Two Independent Events

E X A M P L E 1

Example 2.

You are playing a game that involves spinning the

B

A

A

B

money wheel shown. During your turn you get to

A

A

N

spin the wheel twice. What is the probability that

K

R

you get more than $500 on your first spin and then

U

P

go bankrupt on your second spin?

A

T

A

S

Let event A be getting more than $500

OLUTION

on the first spin, and let event B be going bankrupt

on the second spin. The two events are independent.

A

So, the probability is:

A

8

2

1

P(A and B) = P(A) • P(B) =

•

=

≈ 0.028

2

4

2

4

3

6

A

B

. . . . . . . . . .

The formula given above for the probability of two independent events can be

extended to the probability of three or more independent events.

Probability of Three Independent Events

E X A M P L E 2

B

During the 1997 baseball season, the Florida Marlins won 5 out of 7

ASEBALL

home games and 3 out of 7 away games against the San Francisco Giants. During the

1997 National League Division Series with the Giants, the Marlins played the first

two games at home and the third game away. The Marlins won all three games.

Estimate the probability of this happening.

Source: The Florida Marlins

S

Let events A, B, and C be winning the first, second, and third games.

OLUTION

The three events are independent and have experimental probabilities based on the

regular season games. So, the probability of winning the first three games is:

5

5

3

7

5

P(A and B and C) = P(A) • P(B) • P(C) =

•

•

=

≈ 0.219

7

7

7

3

4

3

730

Chapter 12 Probability and Statistics

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