Learning Objectives

By the end of this lesson, learners should be able to:

  • Apply addition and multiplication rules of probability.
  • Distinguish between mutually exclusive and independent events.
  • Solve business probability problems step by step.

Addition Rule

Used when finding the probability that at least one of two events occurs.

Mutually Exclusive Events

If events cannot occur together:

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

Example

A customer chooses either:

  • Standard delivery (0.70),
  • Express delivery (0.30).

P(Standard or Express) = 0.70 + 0.30 = 1.00

Non-Mutually Exclusive Events

If events can occur together:

P(A or B) = P(A) + P(B) − P(A and B)

Example

  • P(Buys Product A) = 0.40
  • P(Buys Product B) = 0.30
  • P(Buys both) = 0.10

P(A or B) = 0.40 + 0.30 − 0.10 = 0.60

Interpretation: 60% of customers buy at least one of the products.

Multiplication Rule

Independent Events

If events do not affect each other:

P(A and B) = P(A) × P(B)

Example

  • Probability website is available = 0.98
  • Probability payment gateway is available = 0.99

P(Both available) = 0.98 × 0.99 = 0.9702

The online store is expected to be fully operational about 97.02% of the time.

Dependent Events

If one event affects another:

P(A and B) = P(A) × P(B|A)

Example

A bank approves a loan application with probability 0.60. If approved, the probability the customer accepts the loan is 0.80.

P(Approved and Accepted) = 0.60 × 0.80 = 0.48

Interpretation: 48% of applicants are expected to become customers.

Business Case: Supply Chain Reliability

A manufacturer depends on two independent suppliers.

  • Supplier A delivers on time: 0.95
  • Supplier B delivers on time: 0.90

Probability both deliver on time:

0.95 × 0.90 = 0.855

Management recognizes a 14.5% risk that at least one supplier will be late.

Common Mistakes

  • Adding probabilities of non-mutually exclusive events without subtracting overlap.
  • Multiplying probabilities of dependent events as if they were independent.
  • Ignoring conditional information.

Learning Materials / Reference Materials

  • Ross, S. Introduction to Probability Models.
  • MIT OpenCourseWare Probability Notes.

Lesson Summary

Addition and multiplication rules allow analysts to evaluate combined business events such as customer purchases, system reliability, and supply chain performance.

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