## Probability of Exactly Two Events Occurring Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
P(ABC' ∩ AB'C ∩ A'BC) = (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 Two Events - Probability of Occurrence of Exactly Two Events is the fraction of the chance of the intersection of any two of the three given events completing successfully and the third event not completing.
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 complement of the probability of event A occurring.
Probability of Event B - Probability of Event B is the fraction of chance of the given event B completing successfully, according to the given conditions and restrictions.
Probability of Event C - Probability of Event C is the fraction of chance of the given event C completing successfully, according to the given conditions and restrictions.
Probability of Event A - Probability of Event A is the fraction of chance of the given event A completing successfully, according to the given conditions and restrictions.
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 complement of the probability 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 complement of the probability of event C occurring.
STEP 1: Convert Input(s) to Base Unit
Probability of Non-Occurrence of Event A: 0.55 --> No Conversion Required
Probability of Event B: 0.55 --> No Conversion Required
Probability of Event C: 0.3 --> No Conversion Required
Probability of Event A: 0.45 --> No Conversion Required
Probability of Non-Occurrence of Event B: 0.45 --> No Conversion Required
Probability of Non-Occurrence of Event C: 0.7 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P(ABC' ∩ AB'C ∩ A'BC) = (P(A')*P(B)*P(C))+(P(A)*P(B')*P(C))+(P(A)*P(B) *P(C')) --> (0.55*0.55*0.3)+(0.45*0.45*0.3)+(0.45*0.55 *0.7)
Evaluating ... ...
P(ABC' ∩ AB'C ∩ A'BC) = 0.32475
STEP 3: Convert Result to Output's Unit
0.32475 --> No Conversion Required
0.32475 <-- Probability of Occurrence of Exactly Two Events
(Calculation completed in 00.004 seconds)
You are here -
Home » Math »

## 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
Nikita Kumari has verified this Calculator and 600+ more calculators!

## < 10+ Probability of Three Events Calculators

Probability of Atleast One Event Occurring given Probability of Events
Probability of Occurrence of Atleast One Event = 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 None of Events Occurring
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
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
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 Exactly One Event Occurring given Probability of Events
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)
Probability of Exactly Two Events Occurring given Probability of Events
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))
Probability of Atleast One Event Occurring
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
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 Atleast Two Events Occurring given Probability of Events
Probability of Occurrence of Atleast Two Events = (Probability of Event A*Probability of Event B)+((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 All Independent Events Occurring
Probability of Occurrence of All Three Events = Probability of Event A*Probability of Event B*Probability of Event C

## Probability of Exactly Two Events Occurring 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)
P(ABC' ∩ AB'C ∩ A'BC) = (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 Two Events Occurring?

Probability of Exactly Two Events Occurring calculator 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 calculate 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(ABC' ∩ AB'C ∩ A'BC) symbol.

How to calculate Probability of Exactly Two Events Occurring using this online calculator? To use this online calculator 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. Here is how the Probability of Exactly Two Events Occurring calculation can be explained with given input values -> 0.32475 = (0.55*0.55*0.3)+(0.45*0.45*0.3)+(0.45*0.55 *0.7).

### FAQ

What is Probability of Exactly Two Events Occurring?
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 and is represented as P(ABC' ∩ AB'C ∩ A'BC) = (P(A')*P(B)*P(C))+(P(A)*P(B')*P(C))+(P(A)*P(B) *P(C')) or 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 Non-Occurrence of Event A is the likelihood that event A does not happen or the complement of the probability of event A occurring, Probability of Event B is the fraction of chance of the given event B completing successfully, according to the given conditions and restrictions, Probability of Event C is the fraction of chance of the given event C completing successfully, according to the given conditions and restrictions, Probability of Event A is the fraction of chance of the given event A completing successfully, according to the given conditions and restrictions, Probability of Non-Occurrence of Event B is the likelihood that event B does not happen or the complement of the probability of event B occurring & Probability of Non-Occurrence of Event C is the likelihood that event C does not happen or the complement of the probability of event C occurring.
How to calculate Probability of Exactly Two Events Occurring?
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 is calculated using 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 calculate Probability of Exactly Two Events Occurring, you need 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')). With our tool, you need to enter the respective value for 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 Non-Occurrence 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 Two Events?
In this formula, Probability of Occurrence of Exactly Two Events uses 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 Non-Occurrence of Event C. We can use 1 other way(s) to calculate the same, which is/are as follows -
• 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)) Let Others Know