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Old 2022-03-05, 13:18   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

5·233 Posts
Smile 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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