CS202: Discrete Structures

6.4: Conditional Probability and Independent Events

• Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Introduction to Probability" URL

  Focus on the modeling advice and steps 1 - 4 on pages 1 - 9.

• Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Conditional Probability" URL

  Read this lecture. Try to understand the concepts of conditional probability, and just scan the examples. We'll take a closer look at the problems in the next section.

• 6.4.1: Computing a Conditional Probability

  • Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Conditional Probability" URL

    Work through the following examples in this lecture:

    Section 1, "The Halting Problem" (fictitious name of a hockey team) on page 2;

    Section 2.1, "A Coin Problem" on page 6;

    Section 2.2, "A Variant of the Two Coins Problem" on page 8;

    Section 3, "Medical Testing" on page 9;

    Section 4.1, "Carnival Dice" on page 11;

    Section 4.3, "Discrimination Lawsuit" on page 14; and

    Section 4.4, "On-Time Airlines" on page 15.

    Understanding the examples is critical to really understanding conditional probability.

• 6.4.2: Bayes's Theorem

  • University of California, San Diego: Edward Bender and S. Williamson's "Lists, Decisions, and Graphs: Decision Trees and Recursion" URL

    Read Section 3 on pages DT-28 through DT-35.

    Bayes' theorem is a famous theorem for computing conditional probabilities. Assume Ei are mutually exclusive events for i = 1,..., n and U_i E_i = D, for arbitrary event D, P(E_i | D) = P(D | E_i ) P(E_i) / [P(D|E₁)P( E₁) + ....+ P(D|E_n) P(E_n)]. Statements of Bayes' theorem are given on pages DT-28 and DT-32. Like the binomial theorem, Bayes' theorem is very useful in calculating probabilities for many applications, for example, in diagnosis and in decision theory.

• 6.4.3: Computing the Probability of Independent Events

  • Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Independence" URL

    Read this lecture for practice with the probability of independent events.