Mutually Exclusive OutcomesReference > Mathematics > Probability
"Mutually exclusive" is an important concept to understand in probability. Two outcomes are mutually exclusive if they can't both happen at the same time. When we have mutually exclusive outcomes, probabilities are easier to calculate, so most students like mutually exclusive outcome problems better!
I roll a six-sided die, and I get either a 4 or a 5.
The two outcomes are 4 and 5. These are mutually exclusive. Why? Because when you roll the die, the result can't be both 4 and 5 at the same time! It's got to be one or the other.
I roll a six-sided die, and I get either an even number or a prime number.
The two outcomes are "even" and "prime." These are not mutually exclusive. Why? Because 2 is an even number, and it's also a prime number. So it's possible to get a result that is both even and prime.
I flip a coin, and the coin either lands on its edge, or it is a head.
The two outcomes are edge and head. Since these can't both happen at the same time, they are mutually exclusive.
I draw a card from the deck, and it is either black, or it is a queen.
The two outcomes are "black" and "queen." the are not mutually exclusive, because there are two cards that are both black and queens.
For each scenario below, state whether the outcomes are mutually exclusive or not.