W2-slides1

# W2-slides1 - Lecture 4- Outline and Examples (2.5 and 3.2...

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Lecture 4- Outline and Examples ( § 2.5 and § 3.2 in Ross) Sample spaces with equally likely outcomes Conditional Probability

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Equally likely outcomes ( Ross § 2.5) If all outcomes in the sample space are equally likely, then for any event A , P ( A ) = | A | / | S | , i.e., the fraction of outcomes that lie in A .
Example. Flip three coins.

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Example. Flip three coins. There are 8 possible outcomes ( | S | = 8).
Example. Flip three coins. There are 8 possible outcomes ( | S | = 8). Let B =“we get two heads and one tail”

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Example. Flip three coins. There are 8 possible outcomes ( | S | = 8). Let B =“we get two heads and one tail” = { ( H , H , T ) , ( H , T , H ) , ( T , H , H ) } ( | B | = 3 i.e. there are 3 outcomes in B .)
Example. Flip three coins. There are 8 possible outcomes ( | S | = 8). Let B =“we get two heads and one tail” = { ( H , H , T ) , ( H , T , H ) , ( T , H , H ) } ( | B | = 3 i.e. there are 3 outcomes in B .) Then, P ( B ) = 3 / 8.

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Example. (Ross p.53 # 33) A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later, 4 of the 20 elk are captured. What is the probability that 2 of these 4 have been tagged? What assumptions are you making?
Example. (Ross p.53 # 33) A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later, 4 of the 20 elk are captured. What is the probability that 2 of these 4 have been tagged? What assumptions are you making? Solution: We ﬁrst write down our sample set.

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Example. (Ross p.53 # 33) A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later, 4 of the 20 elk are captured. What is the probability that 2 of these 4 have been tagged? What assumptions are you making? Solution: We ﬁrst write down our sample set. S= { all possible groups of 4 elks captured from the population of 20 elks } . | S | =
Example. (Ross p.53 # 33) A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later, 4 of the 20 elk are captured. What is the probability that 2 of these 4 have been tagged? What assumptions are you making? Solution: We ﬁrst write down our sample set. S= { all possible groups of 4 elks captured from the population of 20 elks } . | S | = ± 20 4 ² (unordered, no duplication).

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Example. (Ross p.53 # 33) A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later, 4 of the 20 elk are captured. What is the probability that 2 of these 4 have been tagged? What assumptions are you making? Solution: We ﬁrst write down our sample set. S= { all possible groups of 4 elks captured from the population of 20 elks } . | S | = ± 20 4 ² (unordered, no duplication). We assume that each elk is equally likely to be captured, so each group of 4 elks is equally likely to be captured. So all outcomes in S are equally likely.
Example. (Ross p.53 # 33) continued Our event of interest is A= “2 of the 4 captured elks are tagged”.

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Example. (Ross p.53 # 33) continued Our event of interest is A= “2 of the 4 captured elks are tagged”.
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## This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.

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W2-slides1 - Lecture 4- Outline and Examples (2.5 and 3.2...

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