EXAMPLE 3.6.4

1. Let E be the event: "A randomly chosen person drives a white car."

Let F be the event: "A randomly chosen person has a sister who lives in Alabama."

These events are independent, because there is no apparent reason why a the place of residence of a person's sister would have any influence on a person's car-buying habits. These two conditions do not apparently influence one another.

2. Let E be the event: "Today is your birthday."

Let F be the event: "The fourth digit in your SSN is '7'"

These events are independent, since there is no apparent reason why a certain digit in your SSN should have any connection to whether or not today is your birthday. These two conditions do not influence one another.

3. Let E be the event: "You are wearing a cast on your left arm."

Let F be the event" "Your left arm is broken."

These two events are not independent, because a person wearing a cast is more likely to have a broken limb than is a person who isn't wearing a cast. The occurrence of one of these events affects the probability of the other event. Such events are said to be dependent.

4. Let E be the event: "A randomly chosen voter is a registered Democrat."

Let F be the event: "A randomly chosen voter voted for Bill Clinton."

These events are not independent, because a registered Democrat is more likely to have voted for Bill Clinton than is a person who isn't a registered Democrat. The occurrence of one of these events increases the probability of the other event. Such events are said to be dependent.

5. Let E be the event: "A person is left-handed."

Let F be the event: "A person is right-handed."

Are these events independent?

6. Let E be the event "A person is right-handed."

Let F be the event "A person is named Joe."

Are these events independent?