Probability - Key Concepts & Logic

Disjoint vs independent

Disjoint events can never occur at the same time. For independent events, the outcome of one event does not impact the outcome of the other event. Independent events can occur together.

Disjoint event example

Flipping one coin - heads and tails can not occur at the same time.

Independent events example

In a study of penguins, gender and species - being female does not affect the likelihood a penguin is a King or Emperor penguin.

Addition rule if disjoint

P(A or B) = P(A) + P(B)

Addition rule if not disjoint

P(A or B) = P(A) + P(B) - P(A and B)

Multiplication rule if events are independent

P(A and B) = P(A) * P(B)

Multiplication rule if events are not independent

P(A and B) = P(A) * P(B|A)

How to do conditional probability P(A|B) or P(B|A)?

For P(A|B), Multiply P(A) * P(B). Divide by P(B). This is reversed for P(B|A). Then you would divide A*B by A instead.