Lecture1_Chap2Pt1_1

Lecture1_Chap2Pt1_1 - Chapter2Part1 Probability Examples...

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    Chapter 2 Part 1 Introduction to Probability
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    Probability The study of everyday life. Measure of one’s belief in the  occurrence of a future event.
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    Examples The probability of a new drug lessening pain  caused by arthritis. The probability that the last digit of a student’s  id. number is a seven. The probability that the last digit of two  students’ id. numbers differ by more than one. The probability that the first time a head  appears on repeated coin flips is the sixth flip.
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    Experiments and events We call the actual random phenomenon  an  experiment .   We call the possible outcomes of the  experiment  events . We call the set of all possible outcomes  tha  sample space , denoted by S.
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    Examples An experiment is getting dealt 5 cards.   A three of a kind is an event. An experiment is selecting s student at  random. An event is the last digit of their  id number is a seven. A student taking a test an experiment.   Passing the exam is an event.
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    Big idea of probability Much of probability is the discussion  and manipulation of  sets , or collections  of events.
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    Example Experiment:  Roll a six-sided die and record  the number on which it lands.  Consider the  following sets: A1 = The set of all even numbers. A2 = The set of all multiples of 3. A3 = The set including only the number 4. 
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    In Set Notation A1 ={ x  is an even number between  2 and 6} = {2, 4, 6} A2 = {3,6} A3 = {4} S= {1,2,3,4,5,6}
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    Note! Simple events  are events that cannot  be reduced any further. A1 represents an event.  That is it  represent the outcome of the die  landing on an even number.  However it  is composed of 3 simple events.   Note that A3 was a simple event.
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    Containment -- Subsets
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