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Statistics for finance · level 1

And, or, neither

Independent events multiply for 'and'. For 'or', add and subtract the overlap. For 'neither', take the complement — often the fastest route of the three.

Theory: Probability Foundations

Worked example: Independent events: P(A) = 10%, P(B) = 10%. P(neither happens)?

both1%
at least one19%
neither81%

Step by step

  1. 1

    Both

    10% × 10% = 1%

  2. 2

    At least one

    10 + 10 − 1 = 19%

    Add, then remove the double count.

  3. 3

    Neither

    100 − 19 = 81%

Independent events: P(A) = 10%, P(B) = 10%. P(neither happens)? = 81

The theory behind it

Intuition

Two rules cover most questions: complements (1 − p) and independence (multiply). If events overlap, subtract the overlap once.

Common pitfalls

  • ×Multiplying probabilities that are not independent.
  • ×Double-counting the overlap in an 'or' question.

In the interview

Churn, conversion and failure-rate arithmetic.