4.2 some prob rules

4.2 some prob rules

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  4.2 SOME PROBABILITYRULES – COMPOUND EVENTS PART 1: MULTIPLICATION RULES Chapter 4: Elementary Probability Theory
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  Page 143 Definitions  A compound event consists of two or more simple events.  Two events are independent if the occurrence or non-occurrence of one event does not change the probability that the other event will occur.  If events are dependent, the probability of one event depends upon the occurrence of the other event.  The type of events determines the way we compute the probability of the two events happening together.
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  Page 143 Multiplication Rules  The Event A and B Figure 4-4(a)
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  Page 143 – 144 Conditional Probability  If the events are dependent, then we must take into account the changes in the probability of one event caused by the occurrence of the other event.  Conditional probability is the probability that a dependent event will occur given that another event has occurred.
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  Independence 
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  Page 143 Multiplication Rules  General Multiplication Rule for ANY Events  Use either, depending of the information  Note that the conditional probability rule is contained in both formulas
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  Page How to Use the Multiplication 146 Rules 1. Determine whether A and B are independent events or dependent events. 2. If A and B are independent events P(A and B) = P(A)•P(B) 3. If A and B are any events The multiplication rule forbe independent events can P(A and B) = P(A)•P(B|A)expanded forevents… keep independent more than two or P(A and B) = P(B)•P(A|B)multiplying! The Multiplication Rules apply whenever we want to determine the probability of two events happening together. To indicate “together” we use and between the events. (Page 145)
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  Page Example 4 –Mult. Rule, Independent 144 Events  Suppose you are going to throw two fair dice. What is the probability of getting a 5 on each die? P(5 on 1st die and 5 on 2nd die) = P(5 on 1st die) • P(5 on 2nd die)
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  Page Example 4 –Mult. Rule, Independent 144 Events  Suppose you are going to throw two fair dice. What is the probability of getting a 5 on each die? (use the sample space) 1. Write out the sample space 2. What is the total number of outcomes? 3. How many “favorable” Sample Space for Two Dice outcomes are there? Figure 4-2
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  Page Example 4 –Mult. Rule, Dependent 145 Events  Consider a collection of 6 balls that are identical except in color. There are 3 green balls, 2 blue balls, and 1 red ball. Compute the probability of drawing 2 green balls from the collection if the first ball is not replaced before the second ball is drawn.
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  Solution – Mult.Rule, Dependent Events P( green ball 1st draw and green ball 2nd draw) = P(green on 1st) • P(green on 2nd | green on first) 2: because assuming we got a green ball on 1st draw, there are only 2 left. 5: because if you remove a ball and do not replace, there are only 5 left.
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  Assignment  Page 155  #2, 5, 6, 12, 15, 19, 21, 27(not part f)