How to Calculate Mutually Exclusive Events?
We know that mutually exclusive events are events that can not occur simultaneously and if we take two events A and B as mutually exclusive events and the probability of A is P(A) and the probability of B is P(B) then the probability of happening both events together is,
P(A∩B) = 0
Then the probability of occurring any one event is,
P(AUB) = P(A) or P(B) = P(A) + P(B)
Here, we define ∩ the symbol as the intersection of the set and the U symbol as the union of the set. Before proceeding further let’s learn about the Intersection of the set and the Union of the set.
Intersection of Sets
The symbol which defines the intersection is “∩” it is also called “AND”. We define Intersection as the values that are contained in both sets, i.e.
If A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6}.
Then A intersection B is represented as A∩B and A∩B = {2, 4, 6}
Union of Sets
The symbol which defines the union is “∩” it is also called “OR”. We define Union as all the values contained in both sets, i.e.
If A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6}.
Then A union B is represented as AUB and AUB = {1, 2, 3, 4, 5, 6}
Mutually Exclusive Events
We define mutually exclusive events as events that can never happen simultaneously, i.e. happening an event rules out the possibility of happening the other event. Suppose a cricket match between India and Pakistan can result in the winning of any one team and the loss of the other team both teams can never win the match simultaneously, i.e. if Pakistan wins the match then India definitely loses the match and if India wins the match Pakistan definitely loses the matches thus, we can say Winning of India and Winning of Pakistan both are mutually exclusive events. And occurring one event definitely rules the probability of the other event.
Let’s learn more about mutually exclusive events, their formula, the Venn diagram, and others in detail in this article.
Table of Content
- Mutually Exclusive Events Definition
- How to Calculate Mutually Exclusive Events?
- Probability of Mutually Exclusive Events OR Disjoint Events
- Mutually Exclusive Events Venn Diagram
- Mutually Exclusive Events Probability Rules
- Conditional Probability for Mutually Exclusive Events