Mutually Exclusive Events
What are Mutually Exclusive Events in Probability?
In probability, we define mutually exclusive events as events that can not occur simultaneously. That is if one event happens then it is impossible for another event to happen.
What are examples of Mutually Exclusive Events?
Mutually exclusive events are events that can not occur simultaneously, i.e.
- If we toss a coin, we only get either H or T but we can not get both H and T and hence it is a mutually exclusive event.
- Similarly, if we roll a die it only shows any one of the six faces on the top, and 1 and 2 both can never come on top at once, hence they are mutually exclusive events.
What is the Formula for Mutually Exclusive Events?
Let A and B be two mutually exclusive events and the probability of occurring A is P(A) and the probability of occurring B is P(B), then
P(AUB) = P(A) + P(B)
How to know if A and B are Mutually Exclusive Events?
Two mutually exclusive events are events that can not occur simultaneously. We can say that if A and b are two mutually exclusive events then the intersection of their probability is 0. i.e.
P(A ∩B) = 0
Are Mutually Exclusive Events Independent or Dependent?
Two mutually exclusive events are always dependent in nature. If one event happens, it affects the probability of happening of the other event.
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