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Probability of Exactly Two Events Occurring Formula

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Probability of Occurrence of Exactly Two Events is the likelihood that precisely two out of the three events A,B and C will happen, ensuring that no more or fewer than two events occur. Check FAQs
P(Exactly Two)=(P(A')⋅P(B)⋅P(C))+(P(A)⋅P(B')⋅P(C))+(P(A)⋅P(B)⋅P(C'))
P(Exactly Two) - Probability of Occurrence of Exactly Two Events?P(A') - Probability of Non-Occurrence of Event A?P(B) - Probability of Event B?P(C) - Probability of Event C?P(A) - Probability of Event A?P(B') - Probability of Non-Occurrence of Event B?P(C') - Probability of Non-Occurrence of Event C?

Probability of Exactly Two Events Occurring Example

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Here is how the Probability of Exactly Two Events Occurring equation looks like with Values.

Here is how the Probability of Exactly Two Events Occurring equation looks like with Units.

Here is how the Probability of Exactly Two Events Occurring equation looks like.

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

Probability of Exactly Two Events Occurring Solution

Follow our step by step solution on how to calculate Probability of Exactly Two Events Occurring?

FIRST Step Consider the formula
P(Exactly Two)=(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 Two)=(0.5⋅0.2⋅0.8)+(0.5⋅0.8⋅0.8)+(0.5⋅0.2⋅0.2)
Next Step Prepare to Evaluate
∴ P(Exactly Two)=(0.5⋅0.2⋅0.8)+(0.5⋅0.8⋅0.8)+(0.5⋅0.2⋅0.2)
LAST Step Evaluate
∴P(Exactly Two)=0.42

Probability of Exactly Two Events Occurring Formula Elements

Variables
Probability of Occurrence of Exactly Two Events
Probability of Occurrence of Exactly Two Events is the likelihood that precisely two out of the three events A,B and C will happen, ensuring that no more or fewer than two events occur.
Symbol: P(Exactly Two)
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.
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.

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 Two Events Occurring?

Probability of Exactly Two Events Occurring evaluator uses 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) to evaluate the Probability of Occurrence of Exactly Two Events, The Probability of Exactly Two Events Occurring formula is defined as the likelihood that precisely two out of the three events A,B and C will happen, ensuring that no more or fewer than two events occur. Probability of Occurrence of Exactly Two Events is denoted by P(Exactly Two) symbol.

How to evaluate Probability of Exactly Two Events Occurring using this online evaluator? To use this online evaluator for Probability of Exactly Two Events Occurring, enter Probability of Non-Occurrence of Event A (P(A')), Probability of Event B (P(B)), Probability of Event C (P(C)), Probability of Event A (P(A)), Probability of Non-Occurrence of Event B (P(B')) & Probability of Non-Occurrence of Event C (P(C')) and hit the calculate button.

FAQs on Probability of Exactly Two Events Occurring

What is the formula to find Probability of Exactly Two Events Occurring?
The formula of Probability of Exactly Two Events Occurring is expressed as 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). Here is an example- 0.47 = (0.5*0.2*0.8)+(0.5*0.8*0.8)+(0.5*0.2*0.2).
How to calculate Probability of Exactly Two Events Occurring?
With Probability of Non-Occurrence of Event A (P(A')), Probability of Event B (P(B)), Probability of Event C (P(C)), Probability of Event A (P(A)), Probability of Non-Occurrence of Event B (P(B')) & Probability of Non-Occurrence of Event C (P(C')) we can find Probability of Exactly Two Events Occurring using the formula - 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).
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