What Are Mutually Exclusive Events? (Mathematics Lesson)
What Are Mutually Exclusive Events?
Two events are mutually exclusive if they cannot occur at the same time.If I toss a coin, it cannot land on both Heads and Tails at the same time. Getting a Heads and getting a Tails in a coin toss are mutually exclusive events.
Similarly, if I roll a die, I cannot roll a 1 and a 6 at the same time. Rolling a 1 and rolling a 6 are mutually exclusive events.
Probabilities of Mutually Exclusive Events
Mutually exclusive events are useful in probability.Consider two mutually exclusive events, A and B. It is useful to find the probability of A and B happening, and the probability of A or B happening.

'And'
Mutually exclusive events cannot both happen.
The probability of two mutually exlusive events occuring is 0.
The probability of A and B is 0.
'Or'
The probability of either mutually exclusive events occuring is found by adding the individual probabilities of each event together.
The probability of A or B is the probability of A plus the probability of B.
Real Examples of the Probabilities of Mutually Exclusive Events

'And'
Question: What is the probability of getting a Heads and a Tails in a coin toss?
Getting a Heads and getting a Tails are mutually exclusive events  getting them both together is impossible. Therefore, the probability of getting both is 0.
If H is getting a Heads and T is getting a Tails, then:
'Or'
Question: What is the probability of rolling either a 1 or a 6 on a die?
Rolling a 1 and rolling a 6 are mutually exclusive events. The probability of getting either a 1 or a 6 is the probility of rolling a 1 plus the probability of rolling a 6.
Note: The probability of rolling a 1 is ⅙, as is the probability of rolling a 6.
If 1 is rolling a 1 and 6 is rolling a 6, then:
Visualizing Mutually Exclusive Events on a Venn Diagram
On a Venn Diagram, two mutually exclusive events A and B will be shown as separate, without any intersection.Interactive Test
showNote
WHAT IS PROBABILITY?Probability tells us how likely something is to happen. Probability is given as a number between 0 and 1.
A probability of 0 means an event is impossible.
A probability of 1 means an event is certain.
The closer a probability is to 0 the less likely it is. The closer a probability is to 1 the more likely it is.
A NOTE ON NOTATION
It is often convenient to use a letter to represent an event.For example, in a coin toss, let:
 H be the event getting a Heads, and
 T be the event getting a Tails
Put brackets after the P, and write the letter for the event inside them.
P(H) means the probability of getting Heads.
P(T) means the probability of getting Tails.
"AND/OR" NOTATION
The notation for the probability of A and B happening is:
P(A ∩ B)
The notation for the probability of A or B happening is:
P(A ∪ B)
MORE THAN TWO MUTUALLY EXCLUSIVE EVENTS
It is possible to have more than two mutually exclusive events. Consider rolling a die. Each possible outcome  getting a 1, 2, 3, 4, 5, or 6  is mutually exclusive of any other outcome. Therefore there are 6 mutually exclusive events when rolling a die.To find the probability of an 'or', such as getting a 1 or a 2 or a 3, still involves adding the individual probabilites, only you will have to add three probabilities in this case.