## Probability of Atleast Two Events Occurring given Probability of Events Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
P(AB ∪ AC ∪ BC) = (P(A)*P(B))+((1-P(A))*P(B)*P(C))+(P(A)*(1-P(B))*P(C))
This formula uses 4 Variables
Variables Used
Probability of Occurrence of Atleast Two Events - Probability of Occurrence of Atleast Two Events is the fraction of chance of union of any two of the three given events 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 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.
STEP 1: Convert Input(s) to Base Unit
Probability of Event A: 0.45 --> No Conversion Required
Probability of Event B: 0.55 --> No Conversion Required
Probability of Event C: 0.3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P(AB ∪ AC ∪ BC) = (P(A)*P(B))+((1-P(A))*P(B)*P(C))+(P(A)*(1-P(B))*P(C)) --> (0.45*0.55)+((1-0.45)*0.55*0.3)+(0.45*(1-0.55)*0.3)
Evaluating ... ...
P(AB ∪ AC ∪ BC) = 0.399
STEP 3: Convert Result to Output's Unit
0.399 --> No Conversion Required
0.399 <-- Probability of Occurrence of Atleast Two Events
(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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## < 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 Atleast Two Events Occurring given Probability of Events Formula

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)
P(AB ∪ AC ∪ BC) = (P(A)*P(B))+((1-P(A))*P(B)*P(C))+(P(A)*(1-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 Atleast Two Events Occurring given Probability of Events?

Probability of Atleast Two Events Occurring given Probability of Events calculator uses 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) to calculate the Probability of Occurrence of Atleast Two Events, The Probability of Atleast Two Events Occurring given Probability of Events formula is defined as the likelihood that at least two of the events A, B, or C occurs which means any two or more of these events will happen, considering that they are mutually inclusive independent events, i.e. the events can happen at the same time and 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 Atleast Two Events is denoted by P(AB ∪ AC ∪ BC) symbol.

How to calculate Probability of Atleast Two Events Occurring given Probability of Events using this online calculator? To use this online calculator for Probability of Atleast 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. Here is how the Probability of Atleast Two Events Occurring given Probability of Events calculation can be explained with given input values -> 0.399 = (0.45*0.55)+((1-0.45)*0.55*0.3)+(0.45*(1-0.55)*0.3).

### FAQ

What is Probability of Atleast Two Events Occurring given Probability of Events?
The Probability of Atleast Two Events Occurring given Probability of Events formula is defined as the likelihood that at least two of the events A, B, or C occurs which means any two or more of these events will happen, considering that they are mutually inclusive independent events, i.e. the events can happen at the same time and the outcome of one event does not affect the outcome of another, calculated using probability of events A, B and C and is represented as P(AB ∪ AC ∪ BC) = (P(A)*P(B))+((1-P(A))*P(B)*P(C))+(P(A)*(1-P(B))*P(C)) or 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 Event A is the fraction of chance of the given event A completing successfully, according to the given conditions and restrictions, 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.
How to calculate Probability of Atleast Two Events Occurring given Probability of Events?
The Probability of Atleast Two Events Occurring given Probability of Events formula is defined as the likelihood that at least two of the events A, B, or C occurs which means any two or more of these events will happen, considering that they are mutually inclusive independent events, i.e. the events can happen at the same time and the outcome of one event does not affect the outcome of another, calculated using probability of events A, B and C is calculated using 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). To calculate Probability of Atleast Two Events Occurring given Probability of Events, you need Probability 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 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 Atleast Two Events?
In this formula, Probability of Occurrence of Atleast Two Events uses Probability 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 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) Let Others Know