lec4 - Friday 21st 1 Review Probability Independence Counting Two principles Permutation(ordered sample with re placement without replacement Example A

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Unformatted text preview: Friday, 21st 1. Review: Probability: Independence: Counting: Two principles, Permutation (ordered sample) with re- placement, without replacement Example : A survey question lists seven pizza toppings and ask you to rank your favorite 3. How many possible answers to the survey question are there? One of the choince is 'olives', if all possible rankings are equally likely, what is the possibility that a ran- domly selected suvey has 'olives' in the top 3? Solution : Sample space Ω = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } , n=7, and k=3. Per- mutation since order does matter so P (7 , 3) no replacement. Event with olives is E=(o,*,*),(*,*,o),(*,o,*) and possible answer according to E is P (6 , 2) × 3 and probability is P (6 , 2) /P (7 , 3) . 2. Combinations:(unordered samples) Experiment: A box has n items numbered 1 , ··· ,n . Select k ( ≤ n ) items without replacement. An item is drawn at most onece....
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