[BlindMath] Bayes' Theorem

[pranav.lal at gmail.com]

Dear Jonathan,

Your explanation is just what I was looking for.

One request:
The probability of a random person being infected and testing positive is
whereas the probability of a random person being clear and still testing
positive is  .
The probability that the random person (who has now tested positive)
actually is infected is 0.01998 divided by the total probability that they
were positive (0.01998+0.0294) is therefore

How are we getting the total probability of the person being positive?
Could you put the equation into words and then put in the numbers?

This is the sort of challenge I have run into with many textbooks where I do
not remember where the previous numbers came from so need a refresher of the
formula in words. 

May be this is just me.

If I am confusing you, let me know. This is easier to explain with real time
audio communication. 
Pranav
-----Original Message-----
From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Jonathan Godfrey
via BlindMath
Sent: Monday, January 17, 2022 10:41 AM
To: 'Blind Math list for those interested in mathematics'
<blindmath at nfbnet.org>
Cc: Jonathan Godfrey <A.J.Godfrey at massey.ac.nz>
Subject: [BlindMath] Bayes' Theorem

Hello Pranav and others,

I added an example to the help page for Bayes' Theorem at
https://r-resources.massey.ac.nz/help/bayes.html

This is a classic example where the formula overcomplicates the realities of
working with simple examples. Even expressing the formula in words makes it
uglier than it needs to be.

I haven't used a probability table, but putting the numbers used in my
example into a table might make it much easier to see what is happening.

Hope this helps,
Jonathan


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