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Addition Rule (Mutually Exclusive) Calculator

Rule for finding the probability of either of two mutually exclusive events occurring.

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Probability of A or B

Formula first

Overview

The addition rule for mutually exclusive events states that the probability of either event A or event B occurring is the sum of their individual probabilities. This principle applies strictly when the two events cannot happen at the same time, meaning their intersection is an empty set.

Symbols

Variables

P(A) = Probability of A, P(B) = Probability of B, P(A B) = Probability of A or B

P(A)
Probability of A
Variable
P(B)
Probability of B
Variable
Probability of A or B
Variable

Apply it well

When To Use

When to use: Apply this formula when you are tasked with finding the probability of one of several outcomes occurring, provided those outcomes are disjoint. It is the standard approach for 'OR' logic in probability where the joint probability P(A ∩ B) is known to be zero.

Why it matters: This rule is a cornerstone of probability theory that allows for the construction of more complex statistical models and risk assessments. It enables scientists and economists to aggregate individual risks into a total probability of failure or success within a system.

Avoid these traps

Common Mistakes

  • Adding probabilities for events that are not mutually exclusive.
  • Convert units and scales before substituting, especially percentages, time units, or powers of ten.
  • Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

One free problem

Practice Problem

Practice Problem 1

A standard deck of cards is shuffled. The probability of drawing a King (pA) is 0.077 and the probability of drawing a Queen (pB) is 0.077. What is the probability of drawing either a King or a Queen in a single draw?

Probability of A0.077
Probability of B0.077

Solve for: pAorB

Hint: Since you cannot draw a card that is both a King and a Queen, simply add the two probabilities together.

Practice Problem 2

In a logistics warehouse, the probability that a package is sent to Zone A or Zone B (pAorB) is 0.92. If the probability of a package going to Zone A (pA) is 0.58, what is the probability that it is sent to Zone B (pB), assuming a package cannot go to both?

Probability of A or B0.92
Probability of A0.58

Solve for: pB

Hint: Rearrange the addition rule to solve for the missing individual probability by subtracting pA from the total pAorB.

Practice Problem 3

A spinner has three mutually exclusive sections: Red, Blue, and Green. If the probability of landing on Red (pA) is 0.25 and the probability of landing on Blue (pB) is 0.40, calculate the probability of landing on either Red or Blue.

Probability of A0.25
Probability of B0.4

Solve for: pAorB

Hint: Sum the probabilities of the two distinct outcomes to find the combined probability.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Mutually exclusive events
  2. Wikipedia: Probability theory
  3. Wikipedia: Probability
  4. A First Course in Probability by Sheldon Ross
  5. AQA GCSE Maths — Probability