Sections2.4-2.5-students_SP11

Sections2.4-2.5-students_SP11 - Recap . 1. Product Rule for...

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1 Recap …. 1. Product Rule for k -tuples Counts the number of k -tuples you can create when there are n 1 choices for the first element, . .., n k choices for the k th element: n 1 × n 2 × × n k 2. Permutation Rule Counts the number of permutations of size k that can be created from a set of size n : P k , n = n ! / ( n k )! (order matters!) [ Without Replacement] 3. Combination Rule Counts the number of unordered subsets of size k : (order does not matters!) [ Without Replacement] 1 Section 2.3 Section 2.4, 2.5 2 Today …. Independence: Bayes’ Theorem: Conditional Probability: Law of Total Probability: Next class ….
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2 Conditional Probability In many experiments, knowing that some event has occurred can modify probabilities of other events. Motivating Example: Disease Status and Testing In a given population, 43 people have a particular disease (D+) and 92 people do not have the disease (D-). A test was developed to help identify who has the disease. The outcome of the test can be positive (T+ “ has disease” ) or negative (T- “ does not have disease” ), however the test is not perfect. For a given person, possible outcomes are: D+ and T+ = test correctly identifies disease D+ and T- = test incorrectly says there is no disease (false negative) D- and T- = test correctly says there is no disease D- and T+ = test incorrectly says there is disease (false positive) Sections 2.4-2.5 The number of people in each category in a small population is: Sections 2.4-2.5 The relative frequency in each category :
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Sections2.4-2.5-students_SP11 - Recap . 1. Product Rule for...

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