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Disjoint and Overlapping Events, a la Shmoop It’s a little known fact that most Pirates
miss their mommies.
That’s why every Friday night they kidnap a mommy and roll dice to see who gets to be
read a bedtime story. To play this dice game, the pirates have to
know a little something about Disjoint Events.
Disjoint Events cannot both occur at the same time. If one happens, the other doesn’t.
If a pirate is flying in the air, he is not swimming underwater at the same time.
Disjoint Events are also described as Mutually Exclusive, because the occurrence of one excludes
the occurrence of the other.
Another type of Disjoint Event is a Complementary Event. This is when one event occurs if and
only if the other event does not.
For example, a pirate flips a doubloon. If it is not tails, it must be heads, because
the events are complementary. Overlapping events are events that have one
or more outcomes in common.
For example, if a pirate walks into the bar, there’s a possibility he could be missing
both a leg and an eye. Back to the dice game. Let’s test your pirate
jargon.
How would you describe these events:
Rolling a die and getting an odd number or a 4. Note that the weird bar sign isn't a
typo, that bar sign is just another way for mathematicians to write "or."
They are mutually exclusive, because a 4 cannot be an odd number.
How about rolling a die and getting an odd number or an even number?
They are both mutually exclusive and complementary, because if you don’t get an even number
you get an odd number, and vice versa.
And finally, rolling a die and getting an even number or a four.
They are neither mutually Exclusive nor Complementary. They are overlapping events, though.
Well, looks like this Friday will end like all pirate Fridays.
Nobody understands the convoluted rules of the dice game, so they untie Mommy and have
a big dance party instead.