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?