1. 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. 2 StudyNot StudyTotal Pass.50.20.70 Fail.10.20.30 Total.60.401.0 Joint Probability Table

3. 3 StudyNot StudyTotal Pass.50.20.70 Fail.10.20.30 Total.60.401.0 Are these events independent?

4. 4 Health Insurance AgeYesNo 18 to 34750170 35 and over950130 LetA=18 to 34 age group B=35 and over age group Y=Insurance coverage N=No insurance coverage What is the value of P(A) P(B) P(Y) P(N)? Construct a Joint Probability Table

5. 5 Health Insurance AgeYesNo 18 to 34750170 35 and over950130 Total sample size = 2000 Dividing each entry by 2000 provides the following joint probability table. Health Insurance AgeYesNoTotal 18 to 34.375.085.46 35 and over.475.065.54.850.1501.00 LetA=18 to 34 age group B=35 and over age group Y=Insurance coverage N=No insurance coverage P(A)=.46 P(B) =.54 P(Y) =.85 P(N) =.15