Probability Basics

Addition Rule

For events A and B, avoid double counting overlap with:

P(A∪B) = P(A) + P(B) - P(A∩B)

When events are disjoint, intersection is zero.

Example

Add two event probabilities and subtract their overlap.

highlighted = computed this step

Step 1 — Probability of A

Compute the probability of event A.

P(A)=3/6=12P(A)= 3 / 6 = \hlmath{\frac{1}{2}}

Step 2 — Probability of B

Compute the probability of event B.

P(B)=3/6=12P(B)= 3 / 6 = \hlmath{\frac{1}{2}}

Step 3 — Overlap

Compute the overlap probability.

P(A∩B)=1/6=16P(A\cap B)= 1 / 6 = \hlmath{\frac{1}{6}}

Step 4 — Subtract overlap

Add both probabilities, then subtract the overlap.

P(A∪B)=12+12−16=56P(A\cup B)= \frac{1}{2} + \frac{1}{2} - \frac{1}{6} = \hlmath{\frac{5}{6}}

Step 5 — Result

State the union probability.

P(A∪B)=56P(A\cup B)= \hlmath{\frac{5}{6}}
addition-rule P(A∪B) = P(A) + P(B) - P(A∩B)