Mathematical Methods · probability · manipulative

Does B change P(A)?

A is independent of B when P(A|B) equals P(A) — knowing B happened leaves the chance of A unchanged. Mutually exclusive is a different idea.

Survey responses

Checking independence

Teal / amber highlight is A ∩ B — the cell in both the A row and the B column.

P(A|B) ≈ P(A) dependent mutually exclusive trap

Presets

Counts factor so row shares match column shares — independence holds.

Edit counts

Change any cell (≥ 0). The check under the table updates live.