(20 pts You are trying to estimate the percent of typos in a given document. You
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Question
(20 pts You are trying to estimate the percent of typos in a given document. You go through a document word-by-word until you see the first typo at the 112th word. Assume that typos are independent and occur with the same probability for every word checked. (a) Find the probability of finding a first typo at the 112th word if the probability of a typo is 0.01. (b) Find the probability of finding a first typo at the 112th word if the probability of a typo is 0.1. (c) Document 1 contains 1% typos and document 2 contains 10% typos. You pick one document of the two at random (with equal probability). Given that you observed the first typo on the 112th word, calculate the probability that you picked document 1.Explanation / Answer
a) probabilty that first typo at 112th word =till 111th word no typo*typo error at 112th word
=(1-0.01)111*0.01 =0.0033
b) probabilty that first typo at 112th word =till 111th word no typo*typo error at 112th word
=(1-0.1)111*0.1 =0.0.0000008
c)probabilty that first typo on 112th word =first document and typo at 112th word+second document and typo at 112th word =(1/2)*0.0033+(1/2)*0.0000008 =0.001639
hence probabilty of first document given first typo at 112th word =(1/2)*0.0033/0.001639 =0.999746
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