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 Probability problem using Bayes formula 
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Joined: 27 Feb 2013
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This is taken from Examwise Vol 2 for the 2011 L1 cert. SS02. Q1.
The probability of passing an eye test for people over 70 years old is 80%, and failing is 20%. Fr people under 70 years old the rates are 95% and 5% respectively. 15% of the people tested are over 70 years old.
A report is found of someone failing the test. What is the probability that they are over 70 years old?
Can someone work this out for me? The reason being is I think there is an error in the answer given in the book, and I want to check it.


17 Mar 2013
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Joined: 27 Feb 2013
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andytrader Wrote:
——————————————————-
First you need to find probability of failing
using conditional:

Prob(Fail) = Prob(Fail|=70) + Prob(Fail|
= 20%(15%) + 5%(85%) = 7.25%

Then use Bayes:

Prob(=70|Fail) = [ Prob(Fail|=70)/Prob(Fail) ] *
Prob (=70)

= [20%/7.25%]*15%

= 41.4%
I thought we could get the same answer using tree diagram. If I try using tree diagram for this, I don’t get the same answer. Am I missing anything? Could someone demonstrate the same problem using tree diagram?


17 Mar 2013
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Joined: 20 Apr 2016
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i solved it and had 44.4%,what is the answer provided in whatever source of this question :)


20 Apr 2016
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Joined: 22 Aug 2016
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41.4%


22 Aug 2016
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