Two events are mutually exclusive if they cannot occur simultaneously.
Here are some examples of events which are mutually exclusive:
- Turning left and turning right are mutually exclusive because you cannot do both at the same time
- When you toss a coin, landing on heads or tails are mutually exclusive events
- When choosing a single card, picking a King and an Ace are mutually exclusive
Here are some examples of events which are not mutually exclusive:
- Turning left and scratching your head can happen at the same time
- When choosing a single card; picking a King and a Heart are not mutually exclusive because you can pick a King of Hearts
When two events, A and B, are mutually exclusive it is impossible for them to happen together:
______P(A and B) = 0
______“the probability of A and B happening together equals 0”
The probability of A or B is the sum of the individual probabilities:
______P(A or B) = P(A) + P(B)
______“the probability of A or B equals the probability of A plus the probability of B”.
Example: A Deck of Cards
In a deck of 52 Cards:
______The probability of selecting a King is 1/13, so P(King) = 1/13
______The probability of selecting an Ace is also 1/13, so P(Ace) = 1/13
When we combine those two events:
______The probability of a card being a King and an Ace is 0. (It is impossible.)
______The probability of a card being a King or an Ace is (1/13) + (1/13) = 2/13
This is written like this:
______P(King and Ace) = 0
______P(King or Ace) = 1/13 + 1/13 = 2/13
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This article was written for you by Mia, one of the tutors with Test Prep Academy.