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Mutually Exclusive Outcomes

Reference > 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!

Example One
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.

Example Two
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.

Example Three
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.

Example Four
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.

Questions

1.
I roll a four-sided die, and the result is either a three or a four.
2.
I roll a four-sided die, and the result is either even or a perfect square.
3.
I pick a card from the deck, and it is either a spade or a club.
4.
I pick a card from the deck, and it is either a spade or a nine.
5.
I roll a six-sided die, and the result is either an even number, or it is bigger than four.
6.
I pick a letter from the alphabet, and it is either a vowel or a consonant.
7.
I pick a letter from the alphabet, and it is either a letter in the word "CAT" or it is a letter in the word "DOG."
8.
I pick a letter from the alphabet, and it is either a letter in the word "PUG" or a letter in the word "DOG."
9.
I get to the end of the street and I either turn left or I turn right.
10.
I answer the question, and I either get it wrong or I get it right.
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