2022-03-05, 13:18 | #1 |
"Matthew Anderson"
Dec 2010
Oregon, USA
5·233 Posts |
Bayes's theorem example
Hi again, everyone who is interested in this content,
I worked out a Bayes's Theorem example statistics Bayes's theorem probability P 0<=P<=1 where 1 is certain P(A|B) = [P(B|A) * P(A)] / P(B). in words, the probability of A choose B is dependent on the probability of event A, probability of event B, and probability of B choose A. common example from Chegg and others Suppose there is a school having 60% boys and 40% girls as students. The girls wear trousers or skirts in equal numbers; all boys wear trousers. An observer sees a random student from a distance and this student is wearing trousers. What is the probability of that this student is a girl? recall P(A|B) = [ P(B|A) * P(A) ] / P(B). example details P(G) = 0.4 where G is for girl P(B) = 0.6 where B is for boy P(T|G) = 0.5 probablity of wearing trousers given that the girl is a student, is 0.5 P(T|B) = 1 also, T is for trousers. Find P(G|T) this I can do quickly P(G|T) = P(T|Girl) * P(Girl) / P(Boy) looking above P(G|T) = 0.5 * 0.4 / 0.6. sure of that using calculator on computer desktop give the repeating decimal 0.3333333. This is one third. So, with confidence we see that P(G|T) is about 0.33. see Wikipedia for more explanation Bayes theorem Regards Matt ex engineer, ex school teacher, ex Navy, retired guy |
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