1

Examples of Independent Events

Some examples of independent events are:

Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die. Choosing a marble from a jar AND landing on heads after tossing a coin. Choosing a 3 from a deck of cards, replacing it, AND then choosing an ace as the second card.

Rolling a 4 on a single 6-sided die, AND then rolling a 1 on a second roll of the die.

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

2

Study Not Study Total

Pass .50 .20 .70

Fail .10 .20 .30

Total .60 .40 1.0

( )What is thevalueof Pass Study

( Study)Solve for Pass

( )What is thevalueof Pass Study

Joint Probability Table

3

Study Not Study Total

Pass .50 .20 .70

Fail .10 .20 .30

Total .60 .40 1.0

( ) (.70) (.60) (.50) 0.80Pass Study P P P ( ) ( ) ( ) ( )Pass Study P Pass P Study P Pass Study

( ) (.50)( Study) 0.834

( ) (.60)

P Pass Study PP Pass

P Study P

( ) ( ) ( ) (.60)(.70) (.42)Does Pass Study P Study P Pass Are these events independent?

( ) ( ) ( Study) (.60)(.834) (.50)Pass Study P Study P Pass

4

Health Insurance

Age Yes No

18 to 34 750 170

35 and over 950 130

Let A = 18 to 34 age groupB = 35 and over age

groupY = Insurance coverageN = No insurance

coverage

What is the value of P(A) P(B) P(Y) P(N)?

Construct a Joint Probability Table

(N A), (N B), ( N)Solve for P P P A

5

Health Insurance

Age Yes No

18 to 34 750 170

35 and over 950 130

Total sample size = 2000Dividing each entry by 2000 provides

the following joint probability table.

Health InsuranceAge Yes No Total18 to 34 .375 .085 .4635 and over .475 .065 .54

.850 .150 1.00

Let A = 18 to 34 age groupB = 35 and over age

groupY = Insurance coverageN = No insurance

coverage

(N A) .085(N A) .1848

(A) .46

PP

P

(N B) .065(N B) .1204

(B) .54

PP

P

(A N) .085(A N) .5677

(N) .150

PP

P

P(A) = .46 P(B) = .54 P(Y) = .85 P(N) = .15