## Probability of Exactly One Event Occurring Solution

STEP 0: Pre-Calculation Summary
Formula Used
Probability of Occurrence of Exactly One Event = (Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Non-Occurrence of Event B*Probability of Event C)
P(Exactly One) = (P(A)*P(B')*P(C'))+(P(A')*P(B)*P(C'))+(P(A')*P(B')*P(C))
This formula uses 7 Variables
Variables Used
Probability of Occurrence of Exactly One Event - Probability of Occurrence of Exactly One Event is the likelihood that only one out of the three events A, B and C will happen, ensuring that no more than one event occurs.
Probability of Event A - Probability of Event A is the likelihood that event A happens.
Probability of Non-Occurrence of Event B - Probability of Non-Occurrence of Event B is the likelihood that event B does not happen or the probability of the complement of event B occurring.
Probability of Non-Occurrence of Event C - Probability of Non-Occurrence of Event C is the likelihood that event C does not happen or the probability of the complement of event C occurring.
Probability of Non-Occurrence of Event A - Probability of Non-Occurrence of Event A is the likelihood that event A does not happen or the probability of the complement of event A occurring.
Probability of Event B - Probability of Event B is the likelihood that event B happens.
Probability of Event C - Probability of Event C is the likelihood that event C happens.
STEP 1: Convert Input(s) to Base Unit
Probability of Event A: 0.5 --> No Conversion Required
Probability of Non-Occurrence of Event B: 0.8 --> No Conversion Required
Probability of Non-Occurrence of Event C: 0.2 --> No Conversion Required
Probability of Non-Occurrence of Event A: 0.5 --> No Conversion Required
Probability of Event B: 0.2 --> No Conversion Required
Probability of Event C: 0.8 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P(Exactly One) = (P(A)*P(B')*P(C'))+(P(A')*P(B)*P(C'))+(P(A')*P(B')*P(C)) --> (0.5*0.8*0.2)+(0.5*0.2*0.2)+(0.5*0.8*0.8)
Evaluating ... ...
P(Exactly One) = 0.42
STEP 3: Convert Result to Output's Unit
0.42 --> No Conversion Required
FINAL ANSWER
0.42 <-- Probability of Occurrence of Exactly One Event
(Calculation completed in 00.004 seconds)
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## Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
Dhruv Walia has created this Calculator and 1100+ more calculators!
Verified by Nikita Kumari
The National Institute of Engineering (NIE), Mysuru
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## <Probability of Three Events Calculators

Probability of None of Events Occurring
​ Go Probability of Non Occurrence of Any Event = 1-(Probability of Event A+Probability of Event B+Probability of Event C-(Probability of Event A*Probability of Event B)-(Probability of Event B*Probability of Event C)-(Probability of Event C*Probability of Event A)+(Probability of Event A*Probability of Event B*Probability of Event C))
Probability of Exactly One Event Occurring
​ Go Probability of Occurrence of Exactly One Event = (Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Non-Occurrence of Event B*Probability of Event C)
Probability of Exactly Two Events Occurring
​ Go Probability of Occurrence of Exactly Two Events = (Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Event C)+(Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Event C)+(Probability of Event A*Probability of Event B*Probability of Non-Occurrence of Event C)
Probability of Atleast Two Events Occurring
​ Go Probability of Occurrence of Atleast Two Events = (Probability of Event A*Probability of Event B)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Event C)+(Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Event C)

## <Probability of Two or More Events Calculators

Probability of Exactly One Event Occurring
​ Go Probability of Occurrence of Exactly One Event = (Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Non-Occurrence of Event B*Probability of Event C)
Probability of Atleast One Event Occurring
​ Go Probability of Occurrence of Atleast One Event = Probability of Event A+Probability of Event B+Probability of Event C-Probability of Occurrence of Event A and Event B-Probability of Occurrence of Event B and Event C-Probability of Occurrence of Event A and Event C+Probability of Occurrence of All Three Events
Probability of Atleast Two Events Occurring
​ Go Probability of Occurrence of Atleast Two Events = (Probability of Event A*Probability of Event B)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Event C)+(Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Event C)
Probability of All Independent Events Occurring
​ Go Probability of Occurrence of All Three Events = Probability of Event A*Probability of Event B*Probability of Event C

## Probability of Exactly One Event Occurring Formula

Probability of Occurrence of Exactly One Event = (Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Non-Occurrence of Event B*Probability of Event C)
P(Exactly One) = (P(A)*P(B')*P(C'))+(P(A')*P(B)*P(C'))+(P(A')*P(B')*P(C))

## What is Probability?

In Mathematics, Probability theory is the study of chances. In real life, we predict chances depending on the situation. But Probability theory is bringing a mathematical foundation for the concept of Probability. For example, if a box contain 10 balls which include 7 black balls and 3 red balls and randomly chosen one ball. Then the Probability of getting red ball is 3/10 and Probability of getting black ball is 7/10. When coming to statistics, Probability is like the back bone of statistics. It has a wide application in decision making, data science, business trend studies, etc.

## How to Calculate Probability of Exactly One Event Occurring?

Probability of Exactly One Event Occurring calculator uses Probability of Occurrence of Exactly One Event = (Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Non-Occurrence of Event B*Probability of Event C) to calculate the Probability of Occurrence of Exactly One Event, The Probability of Exactly One Event Occurring formula is defined as the likelihood that only one out of the three events A, B and C will happen, ensuring that no more than one event occurs. Probability of Occurrence of Exactly One Event is denoted by P(Exactly One) symbol.

How to calculate Probability of Exactly One Event Occurring using this online calculator? To use this online calculator for Probability of Exactly One Event Occurring, enter Probability of Event A (P(A)), Probability of Non-Occurrence of Event B (P(B')), Probability of Non-Occurrence of Event C (P(C')), Probability of Non-Occurrence of Event A (P(A')), Probability of Event B (P(B)) & Probability of Event C (P(C)) and hit the calculate button. Here is how the Probability of Exactly One Event Occurring calculation can be explained with given input values -> 0.67 = (0.5*0.8*0.2)+(0.5*0.2*0.2)+(0.5*0.8*0.8).

### FAQ

What is Probability of Exactly One Event Occurring?
The Probability of Exactly One Event Occurring formula is defined as the likelihood that only one out of the three events A, B and C will happen, ensuring that no more than one event occurs and is represented as P(Exactly One) = (P(A)*P(B')*P(C'))+(P(A')*P(B)*P(C'))+(P(A')*P(B')*P(C)) or Probability of Occurrence of Exactly One Event = (Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Non-Occurrence of Event B*Probability of Event C). Probability of Event A is the likelihood that event A happens, Probability of Non-Occurrence of Event B is the likelihood that event B does not happen or the probability of the complement of event B occurring, Probability of Non-Occurrence of Event C is the likelihood that event C does not happen or the probability of the complement of event C occurring, Probability of Non-Occurrence of Event A is the likelihood that event A does not happen or the probability of the complement of event A occurring, Probability of Event B is the likelihood that event B happens & Probability of Event C is the likelihood that event C happens.
How to calculate Probability of Exactly One Event Occurring?
The Probability of Exactly One Event Occurring formula is defined as the likelihood that only one out of the three events A, B and C will happen, ensuring that no more than one event occurs is calculated using Probability of Occurrence of Exactly One Event = (Probability of Event A*Probability of Non-Occurrence of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Event B*Probability of Non-Occurrence of Event C)+(Probability of Non-Occurrence of Event A*Probability of Non-Occurrence of Event B*Probability of Event C). To calculate Probability of Exactly One Event Occurring, you need Probability of Event A (P(A)), Probability of Non-Occurrence of Event B (P(B')), Probability of Non-Occurrence of Event C (P(C')), Probability of Non-Occurrence of Event A (P(A')), Probability of Event B (P(B)) & Probability of Event C (P(C)). With our tool, you need to enter the respective value for Probability of Event A, Probability of Non-Occurrence of Event B, Probability of Non-Occurrence of Event C, Probability of Non-Occurrence of Event A, Probability of Event B & Probability of Event C and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Probability of Occurrence of Exactly One Event?
In this formula, Probability of Occurrence of Exactly One Event uses Probability of Event A, Probability of Non-Occurrence of Event B, Probability of Non-Occurrence of Event C, Probability of Non-Occurrence of Event A, Probability of Event B & Probability of Event C. We can use 1 other way(s) to calculate the same, which is/are as follows -
• Probability of Occurrence of Exactly One Event = (Probability of Event A*(1-Probability of Event B)*(1-Probability of Event C))+((1-Probability of Event A)*Probability of Event B*(1-Probability of Event C))+((1-Probability of Event A)*(1-Probability of Event B)*Probability of Event C)
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