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We subtract the intersection because adding the individual probabilities $P(E)$ and $P(F)$ counts the overlapping region twice. Subtracting $P(E \cap F)$ once corrects this double-counting so that every outcome in the union is counted exactly once.

Conditions: E and F are overlapping events in a probability space.

We subtract the intersection because adding the individual probabilities $P(E)$ and $P(F)$ counts the overlapping region twice. Subtracting $P(E \cap F)$ once corrects this double-counting so that every outcome in the union is counted exactly once.

Conditions: E and F are overlapping events in a probability space.

A probability must be a number between 0 and 1 inclusive. A percent value, such as 10, represents a whole number and falls outside this valid range.

Conditions: The value is intended to represent a probability.

A probability must be a number between 0 and 1 inclusive. A percent value, such as 10, represents a whole number and falls outside this valid range.

Conditions: The value is intended to represent a probability.

It is recommended to delay fraction simplification because all terms in the equation share a common denominator. Keeping the fractions unsimplified makes the addition and subtraction steps much easier and less prone to arithmetic errors.

Conditions: All probability terms in the equation share the same denominator.

It is recommended to delay fraction simplification because all terms in the equation share a common denominator. Keeping the fractions unsimplified makes the addition and subtraction steps much easier and less prone to arithmetic errors.

Conditions: All probability terms in the equation share the same denominator.