Chapter Contents

Following are the original SNB files (.tex or .rap) used in making this chapter. For more information, go to SNB info.

SNB files: 1. Factorial Notation (SNB)

2. Basic Principles of Counting (SNB)

3. Permutations (SNB)

4. Combinations (SNB)

5. Introduction to Probability Theory (SNB)

6. Probability of an Event (SNB)

Singapore TOTO (SNB)

Probability and Poker (SNB)

7. Conditional Probability (SNB)

8. Independent and Dependent Events (SNB)

9. Mutually Exclusive Events (SNB)

10. Bayes’ Theorem (SNB)

11. Probability Distributions - Concepts (SNB)

12. Binomial Probability Distributions (SNB)

13. Poisson Probability Distribution (SNB)

14. Normal Probability Distribution (SNB)

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7. Conditional Probability

If E₁ and E₂ are two events, the probability that E₂ occurs given that E₁ has occurred is denoted by P(E₂|E₁).

P(E₂|E₁) is called the conditional probability of E₂ given that E₁ has occurred.

Calculating Conditional Probability

Let E₁ and E₂ be any two events defined in a sample space S such that P(E₁) > 0.

The conditional probability of E₂, assuming E₁ has already occurred, is given by

EXAMPLE 1

Let A denote the event `student is female' and let B denote the event `student is French'. In a class of 100 students suppose 60 are French, and suppose that 10 of the French students are females. Find the probability that if I pick a French student, it will be a girl, that is, find P(A|B).

Answer

EXAMPLE 2

What is the probability that the total of two dice will be greater than 8, given that the first die is a 6?

Answer

Probability and Poker

8. Independent and Dependent Events

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