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Probability of Exactly One Event Occurring Formula

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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. Check FAQs
P(Exactly One)=(P(A)⋅P(B')⋅P(C'))+(P(A')⋅P(B)⋅P(C'))+(P(A')⋅P(B')⋅P(C))
P(Exactly One) - Probability of Occurrence of Exactly One Event?P(A) - Probability of Event A?P(B') - Probability of Non-Occurrence of Event B?P(C') - Probability of Non-Occurrence of Event C?P(A') - Probability of Non-Occurrence of Event A?P(B) - Probability of Event B?P(C) - Probability of Event C?

Probability of Exactly One Event Occurring Example

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Here is how the Probability of Exactly One Event Occurring equation looks like with Values.

Here is how the Probability of Exactly One Event Occurring equation looks like with Units.

Here is how the Probability of Exactly One Event Occurring equation looks like.

0.42Edit=(0.5Edit⋅0.8Edit⋅0.2Edit)+(0.5Edit⋅0.2Edit⋅0.2Edit)+(0.5Edit⋅0.8Edit⋅0.8Edit)
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Home » Math » Probability and Disribution » Probability » Probability of Exactly One Event Occurring

Probability of Exactly One Event Occurring Solution

Follow our step by step solution on how to calculate Probability of Exactly One Event Occurring?

FIRST Step Consider the formula
P(Exactly One)=(P(A)⋅P(B')⋅P(C'))+(P(A')⋅P(B)⋅P(C'))+(P(A')⋅P(B')⋅P(C))
Next Step Substitute values of Variables
∴ P(Exactly One)=(0.5⋅0.8⋅0.2)+(0.5⋅0.2⋅0.2)+(0.5⋅0.8⋅0.8)
Next Step Prepare to Evaluate
∴ P(Exactly One)=(0.5⋅0.8⋅0.2)+(0.5⋅0.2⋅0.2)+(0.5⋅0.8⋅0.8)
LAST Step Evaluate
∴P(Exactly One)=0.42

Probability of Exactly One Event Occurring Formula Elements

Variables
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.
Symbol: P(Exactly One)
Measurement: NAUnit: Unitless
Note: Value should be between 0 to 1.
Probability of Event A
Probability of Event A is the likelihood that event A happens.
Symbol: P(A)
Measurement: NAUnit: Unitless
Note: Value should be between 0 to 1.
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.
Symbol: P(B')
Measurement: NAUnit: Unitless
Note: Value should be between 0 to 1.
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.
Symbol: P(C')
Measurement: NAUnit: Unitless
Note: Value should be between 0 to 1.
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.
Symbol: P(A')
Measurement: NAUnit: Unitless
Note: Value should be between 0 to 1.
Probability of Event B
Probability of Event B is the likelihood that event B happens.
Symbol: P(B)
Measurement: NAUnit: Unitless
Note: Value should be between 0 to 1.
Probability of Event C
Probability of Event C is the likelihood that event C happens.
Symbol: P(C)
Measurement: NAUnit: Unitless
Note: Value should be between 0 to 1.

Credits

Creator Image
Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
Dhruv Walia has created this Formula and 1100+ more formulas!
Verifier Image
Verified by Nikita Salampuria
The National Institute of Engineering (NIE), Mysuru
Nikita Salampuria has verified this Formula and 600+ more formulas!

Other formulas in Probability of Three Events category

​Go Probability of All Independent Events Occurring
P(A∩B∩C)=P(A)⋅P(B)⋅P(C)
​Go Probability of Atleast One Event Occurring
P(A∪B∪C)=P(A)+P(B)+P(C)-P(A∩B)-P(B∩C)-P(A∩C)+P(A∩B∩C)

How to Evaluate Probability of Exactly One Event Occurring?

Probability of Exactly One Event Occurring evaluator 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 evaluate 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 evaluate Probability of Exactly One Event Occurring using this online evaluator? To use this online evaluator 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.

FAQs on Probability of Exactly One Event Occurring

What is the formula to find Probability of Exactly One Event Occurring?
The formula of Probability of Exactly One Event Occurring is expressed as 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). Here is an example- 0.67 = (0.5*0.8*0.2)+(0.5*0.2*0.2)+(0.5*0.8*0.8).
How to calculate Probability of Exactly One Event Occurring?
With 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)) we can find Probability of Exactly One Event Occurring using the 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).
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