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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)=((1-P(A))⋅P(B)⋅P(C))+(P(A)⋅(1-P(B))⋅P(C))+(P(A)⋅P(B)⋅(1-P(C)))
P(Exactly Two) - Probability of Occurrence of Exactly Two Events?P(A) - Probability of Event A?P(B) - Probability of Event B?P(C) - Probability of Event C?

Probability of Exactly Two Events Occurring given Probability of Events Example

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

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

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

0.42Edit=((1-0.5Edit)⋅0.2Edit⋅0.8Edit)+(0.5Edit⋅(1-0.2Edit)⋅0.8Edit)+(0.5Edit⋅0.2Edit⋅(1-0.8Edit))
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HomeIcon Home » Category Math » Category Probability and Disribution » Category Probability » fx Probability of Exactly Two Events Occurring given Probability of Events

Probability of Exactly Two Events Occurring given Probability of Events Solution

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

FIRST Step Consider the formula
P(Exactly Two)=((1-P(A))⋅P(B)⋅P(C))+(P(A)⋅(1-P(B))⋅P(C))+(P(A)⋅P(B)⋅(1-P(C)))
Next Step Substitute values of Variables
∴ P(Exactly Two)=((1-0.5)⋅0.2⋅0.8)+(0.5⋅(1-0.2)⋅0.8)+(0.5⋅0.2⋅(1-0.8))
Next Step Prepare to Evaluate
∴ P(Exactly Two)=((1-0.5)⋅0.2⋅0.8)+(0.5⋅(1-0.2)⋅0.8)+(0.5⋅0.2⋅(1-0.8))
LAST Step Evaluate
∴P(Exactly Two)=0.42

Probability of Exactly Two Events Occurring given Probability of Events 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.
Formulas to find Probability of Occurrence of Exactly Two EventsOpen Variable
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.
Formulas to find Probability of Event AOpen Variable
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.
Formulas to find Probability of Event BOpen Variable
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.
Formulas to find Probability of Event COpen Variable

Other Formulas to find Probability of Occurrence of Exactly Two Events

​Go Probability of Exactly Two Events Occurring
P(Exactly Two)=(P(A')⋅P(B)⋅P(C))+(P(A)⋅P(B')⋅P(C))+(P(A)⋅P(B)⋅P(C'))

Other formulas in Probability of Three Events category

​Go Probability of None of Events Occurring
P((A∪B∪C)')=1-(P(A)+P(B)+P(C)-(P(A)⋅P(B))-(P(B)⋅P(C))-(P(C)⋅P(A))+(P(A)⋅P(B)⋅P(C)))
​Go Probability of Exactly One Event Occurring
P(Exactly One)=(P(A)⋅P(B')⋅P(C'))+(P(A')⋅P(B)⋅P(C'))+(P(A')⋅P(B')⋅P(C))
​Go Probability of Atleast Two Events Occurring
P(Atleast Two)=(P(A)⋅P(B))+(P(A')⋅P(B)⋅P(C))+(P(A)⋅P(B')⋅P(C))
​Go Probability of Atleast One Event Occurring given Probability of Events
P(A∪B∪C)=P(A)+P(B)+P(C)-(P(A)⋅P(B))-(P(B)⋅P(C))-(P(C)⋅P(A))+(P(A)⋅P(B)⋅P(C))

How to Evaluate Probability of Exactly Two Events Occurring given Probability of Events?

Probability of Exactly Two Events Occurring given Probability of Events evaluator uses Probability of Occurrence of Exactly Two Events = ((1-Probability of Event A)*Probability of Event B*Probability of Event C)+(Probability of Event A*(1-Probability of Event B)*Probability of Event C)+(Probability of Event A*Probability of Event B*(1-Probability of Event C)) to evaluate the Probability of Occurrence of Exactly Two Events, The Probability of Exactly Two Events Occurring given Probability of Events 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, considering that they are independent events, i.e. the outcome of one event does not affect the outcome of another, calculated using probability of events A, B and C. Probability of Occurrence of Exactly Two Events is denoted by P(Exactly Two) symbol.

How to evaluate Probability of Exactly Two Events Occurring given Probability of Events using this online evaluator? To use this online evaluator for Probability of Exactly Two Events Occurring given Probability of Events, enter Probability 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 Two Events Occurring given Probability of Events

What is the formula to find Probability of Exactly Two Events Occurring given Probability of Events?
The formula of Probability of Exactly Two Events Occurring given Probability of Events is expressed as Probability of Occurrence of Exactly Two Events = ((1-Probability of Event A)*Probability of Event B*Probability of Event C)+(Probability of Event A*(1-Probability of Event B)*Probability of Event C)+(Probability of Event A*Probability of Event B*(1-Probability of Event C)). Here is an example- 0.42 = ((1-0.5)*0.2*0.8)+(0.5*(1-0.2)*0.8)+(0.5*0.2*(1-0.8)).
How to calculate Probability of Exactly Two Events Occurring given Probability of Events?
With Probability of Event A (P(A)), Probability of Event B (P(B)) & Probability of Event C (P(C)) we can find Probability of Exactly Two Events Occurring given Probability of Events using the formula - Probability of Occurrence of Exactly Two Events = ((1-Probability of Event A)*Probability of Event B*Probability of Event C)+(Probability of Event A*(1-Probability of Event B)*Probability of Event C)+(Probability of Event A*Probability of Event B*(1-Probability of Event C)).
What are the other ways to Calculate Probability of Occurrence of Exactly Two Events?
Here are the different ways to Calculate Probability of Occurrence of Exactly Two Events-
  • 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)OpenImg
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