Lecture Notes Chapter 2 Section2.4

Lecture Notes Chapter 2 Section2.4 -...

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Once again, consider the tossing of a fair 6-sided  die, and let A be the event “an even number is  observed.”   Then This “definition” of probability will work as long as  the sample space is finite. To use this definition, it is important to be able to  count the number of outcomes in A. outcomes of number Total A in outcomes of Number 6 3 P(A) = =
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The first counting principle we will look at is called  the  multiplication principle  it states: If the first task of an experiment can result in n 1   possible outcomes and, for each such outcome,  the second task can result in n 2  possible  outcomes, then there are n 1 n 2  possible outcomes  for the two tasks together. Tree diagrams are often helpful in verifying the  multiplication principle and for listing outcomes of  events.
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Example 1:  A pizza parlor offers thin crust,  original crust, and thick crust; they also offer  marinara sauce and original tomato sauce; as for  toppings they offer pepperoni, mushrooms,  sausage, anchovies, hamburger, green peppers,  and black olives.  How many different 1-topping  pizzas can this parlor make? Solution: There are 3 choices for the type of crust,  2 choices of sauce, and 7 choices of topping. Thus the total number of 1-topping pizzas is equal  to 3 * 2 * 7 = 42 different pizzas. 
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Example 2:  Suppose a new firm is deciding  where to build two new plants – one in the east  and one in the west.  Four eastern cities and two  western cities are possible locations.  How many  possibilities for locating the two plants are there? There are 8 possibilities.
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Example 3:  From the previous example, what is  the probability that city A or city E gets selected? Solution:  Going back to the tree diagram, count 
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This note was uploaded on 02/04/2011 for the course MATH 1780 taught by Professor Snyder during the Fall '08 term at North Texas.

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Lecture Notes Chapter 2 Section2.4 -...

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