STA 301 - Ch 02 - pp 33-43

STA 301 - Ch 02 - pp 33-43 - Chapter 2: Probability...

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Chapter 2: Probability 33 PROBABILITY The Frequentist Notion of Probability Consider a process that can be repeated over and over again (forever), independently and under the same conditions. Probability describes the relative frequencies at which all possible outcomes of the process occur. These outcome probabilities are on a scale of 0 (never occurs) to 1 (always occurs), and the sum of all outcome probabilities must be 1. Probability of an event the probability of an event A is the sum of the probabilities of all sample points in A . We have the following propertes: ( 29 1 0 A P ( 29 0 = φ P ( 29 1 = S P And, if K , , , 3 2 1 A A A is a sequence of mutually exclusive events, then ( 29 ( 29 ( 29 ( 29 L L U U U + + + = 3 2 1 3 2 1 A P A P A P A A A P If an experiment has N equally likely outcomes and exactly n of those outcomes correspond to event A , then the probability of event A is ( 29 N n A P = Example 1: a) What is the chance of rolling a 5 with a fair, six-sided die? b) What is the chance of drawing the queen of spades from a deck of 52 cards? c) What is the chance of drawing a queen? d) What is the chance of rolling an even number with a fair, six-sided die?
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Chapter 2: Probability 34 Example 2: (p. 50, example 2.24) A die is loaded in such a way that an even number is twice as likely to occur as an odd number. If E is the event that a number less than 4 occurs on a single toss of the die, find P(E) . Example 3: Two fair, six-sided dice are rolled. What is the chance of getting… (a) a total of 4 spots? (b) a total of 7 spots?
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Chapter 2: Probability 35 Addition Rule The addition rule is used to determine the chance that either (or both) of two events occurs. In general, ( 29 ( 29 ( 29 ( 29 B A P B P A P B A P I U - + = Notice that if the two events are mutually exclusive , then ( 29 ( 29 0 = = φ P B A P I , so we can simplify to ( 29 ( 29 ( 29 B P A P B A P + = U In the general formula, the ( 29 B A P I term is subtracted to avoid double-counting. This can be easily illustrated using Venn diagrams. In each of the diagrams below, the left circle represents event A, and the right circle represents event B. In the left diagram, events A and B overlap.
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STA 301 - Ch 02 - pp 33-43 - Chapter 2: Probability...

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