Lecture 8

# Lecture 8 - marbles without replacement What is the...

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Counting Often we need to determine the number of elements in the sample space, S or in an event, E. Here are some useful techniques presented by example. 1. If you have 9 choices for an exterior car color and 4 choices for an interior car color, how many different color ways can you order your car? 2. If there are 8 contestants, how many different ways can first, second and third place prizes be awarded?

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Factorials n! = (n)*(n-1)*(n-2)*. ..*2*1
Combinations The number of ways to select r items from a group of n items when order is not important. ( 29 ! !( )! n n r r n C r n r = = - 3. If we wish to select a committee of 3 from 5 people, how many ways could this be done?

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Example 2:
We select 3 marbles from a box that has 4 red marbles and 7 black

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Unformatted text preview: marbles, without replacement . What is the probability that we select 3 red marbles? P(Three Red )= # of ways for 3 Reds total # of ways to pick 3 P(Two Red and one Black) = Recall: The complement of an event A includes all events that are not part of the event A. Denoted A ′ (or sometimes c A ) P( c A ) = 1- P(A) P(A) = 1- P( c A ) Returning to the marble example: 4 Red, 7 Black Marbles We are selecting 3 marbles. What is the probabilility that at least one will be red? At least one={1red, 2red, 3red} P(At least one Red) = P(1 red) + P(2 red) + P(3 red) This is a lot of calculation. Using the complement rule, we get P(At least one Red) = 1 – P(no Red )...
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## This note was uploaded on 02/15/2009 for the course STAT 2004 taught by Professor Melutz during the Fall '07 term at Virginia Tech.

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Lecture 8 - marbles without replacement What is the...

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