Probability Basics

Mutually Exclusive Events

If events are disjoint (cannot happen together), intersection probability is zero.

P(M∪N) = P(M) + P(N)

Example

For events with no overlap, add the probabilities.

highlighted = computed this step

Step 1 — Probability of A

Compute the probability of event A.

P(A)=2/6=13P(A)= 2 / 6 = \hlmath{\frac{1}{3}}

Step 2 — Probability of B

Compute the probability of event B.

P(B)=2/6=13P(B)= 2 / 6 = \hlmath{\frac{1}{3}}

Step 3 — No overlap

Mutually exclusive events have no overlap.

P(A∩B)=0P(A\cap B)= \hl{0}

Step 4 — Add probabilities

Add the probabilities without subtracting overlap.

P(A∪B)=13+13=23P(A\cup B)= \frac{1}{3} + \frac{1}{3} = \hlmath{\frac{2}{3}}

Step 5 — Result

State the mutually exclusive union probability.

P(A∪B)=23P(A\cup B)= \hlmath{\frac{2}{3}}
mutually-exclusive P(M∪N) = P(M) + P(N)