← Apply probability concepts

4 Independence & conditional

Testing independence

  • A and B are independent if P(A | B) = P(A): knowing B doesn’t change A.
  • Equivalently, independent ⟺ P(A and B) = P(A) × P(B).
  • Mutually exclusive (can’t both happen) is different. Those events are NOT independent.
Worked example Conditional from a two-way table Of 200 people: 120 own a car; of those, 90 also own a bike. Find P(bike | car). P(bike and car) uses the 90 who own both. P(bike | car) = (owns both) / (owns car) = 90/120. = 0.75. ✓ P(bike | car) = 0.75.

A fast check before testing independence

  • Have I calculated P(A | B) AND compared it directly with P(A), rather than just asserting independence?
  • Am I confusing "mutually exclusive" with "independent" — the two are never the same thing?

Practise just this