Probability Rules

OR rule

• When you see “A or B”

• The problem asks for the probability of either of events occurring.

AND rule

• When you see “A and B”

• The problem asks for the ability of both the events occurring together.

Complement Rule

Use when → “At least one defective”

Mutually Exclusive Events

• If the events cannot occur simultaneously.

• P(A ∩ B) = 0

Independent Events

If P(A ∩ B) = P(A) × P(B)

Dependent Events

If P(A|B) =/= P(A)

Permutation problem

• “Arrange”

• “Order”

• “Sequence”

• “Lineup

• Order matters

Combination Problem

• “Choose”

• “Select”

• “Sample”

• “Group”

• Order does not matter

Counting Principle Problem

• Each step involves choices multiplied together

• Example #1: Licensed plate digits

• Example #2: Multiple-choice exams

Condition Probability Problem

• “Given that”

• “Provided that”

• Example: Given that a component passed test A, find the probability it passes test B

Bayes’ Theorem Problem

• Involved reversing conditional probability

• Finding P(A|B) when given with P(B|A)

• Common in medical tests, reliability, or to detect classification

• Example: If a test defects 95% of the time, but false positives occur 5%, find the true probability a defective part caused a faulty a positive test.