GeneralProbabilityGCSE
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Probability (Non-Mutually Exclusive Events) Calculator

Calculates the probability of event A or event B occurring when they can both happen.

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Probability of A or B

Formula first

Overview

This formula, often called the Addition Rule for Probability, determines the likelihood of at least one of two events (A or B) occurring when these events are not mutually exclusive, meaning they can happen at the same time. It sums the individual probabilities of A and B, then subtracts the probability of both A and B occurring (P(A ∩ B)) to avoid double-counting the overlap.

Symbols

Variables

P(A) = Probability of Event A, P(B) = Probability of Event B, P(A \cap B) = Probability of A and B, P(A \cup B) = Probability of A or B

Probability of Event A
Probability of Event B
Probability of A and B
Probability of A or B

Apply it well

When To Use

When to use: Apply this formula when you need to find the probability of 'A OR B' and you know that events A and B can occur simultaneously. This is common in scenarios involving overlapping sets, such as drawing cards, analyzing survey data, or predicting outcomes where multiple conditions might be met.

Why it matters: Understanding the probability of non-mutually exclusive events is fundamental in statistics, risk assessment, and decision-making. It allows for accurate prediction in complex systems, from medical diagnostics (probability of having disease X or symptom Y) to financial modeling (probability of stock A rising or stock B falling). It's essential for avoiding overestimation of probabilities when events overlap.

Avoid these traps

Common Mistakes

  • Forgetting to subtract P(A ∩ B), leading to double-counting the overlap.
  • Confusing mutually exclusive events with non-mutually exclusive events.
  • Incorrectly calculating P(A ∩ B) or assuming it's always P(A) * P(B) (which is only true for independent events).

One free problem

Practice Problem

In a class, the probability of a student liking chocolate (A) is 0.6, and the probability of liking vanilla (B) is 0.4. The probability of liking both is 0.2. What is the probability that a randomly chosen student likes chocolate or vanilla?

Probability of Event A0.6
Probability of Event B0.4
Probability of A and B0.2

Solve for: P_A_union_B

Hint: Remember to subtract the overlap to avoid double-counting.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Addition rule of probability
  2. Britannica: Probability
  3. Wikipedia: Probability
  4. Sheldon Ross, A First Course in Probability
  5. GCSE Mathematics Textbooks (e.g., AQA GCSE (9-1) Mathematics Higher Student Book)