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Chapter4
February 21, 2012
Chapter 4: Probability
Section 41: Review and Preview
The Rare Event Rule: If, under a given assumption, the probability of an event happening is extremely small, then the assumption is probably incorrect.
Chapter4
February 21, 2012
Section 42: Basic Concepts of Probability
Definitions:
• A probability experiment is a random procedure with certain possible outcomes. • The sample space is the set of all possible outcomes. • An event is a group of outcomes. • A simple event is a unique outcome.
Chapter4
February 21, 2012
Example: Flip three fair coins (penny, nickel, and dime).
1. What is the sample space?
2. Are the following simple events or not?
a. All coins show heads.
b. Exactly one coin shows heads.
c. At least one coin shows tails.
Chapter4
February 21, 2012
Notation:
A, B, C, etc. are events. (Avoid P and S.)
P(A) is the probability that event A occurs.
How to Calculate Probabilities:
1. Relative Frequency Approach (approximation):
The probability experiment is done repeated n times and event A occurs f times, then f P(A) ≈ n
Example: A basketball player makes 19 free throws and misses 8 free throws. What is his free throw percentage?
Chapter4
February 21, 2012
2. Classical Approach:
Suppose all the outcomes in the sample space have an equal chance of occurring. If s of the outcomes mean that event A happens and n is the size of the sample space then s P(A) = n
Examples:
1. Three fair coins are flipped. Find the probability of getting exactly one head.
2. A straight flush in poker is a hand with 5 cards where all the cards are the same suit and the ranks of the cards are consecutive (Ace ...