Tree Diagram Trials

Tree: P(A and B) = P(A) × P(B | A).

Without replacement: the bag loses one counter after the first draw.

Independent events: P(B | A) = P(B). Mutually exclusive events cannot occur together.

Possibility diagram: probability = favourable outcomes ÷ equally likely outcomes.

Expected frequency: E = np. Typical random variation is measured using √[np(1 − p)].

Graph: observed relative frequency = successes ÷ trials. The horizontal dashed line is theoretical probability; the horizontal axis uses a base-10 logarithmic scale.