Reply To: The Riddle Thread….

squeak and ICOT-

The method is correct but I like to set it up differently.

This riddle falls under the category of Bayesian Estimation with a Discrete Prior. (Sounds innocent to me?)

I like setting it up in a table like a spreadsheet.

There is one column for each category, in this case two.

Line one is the “Prior Probability”, or the probability of being in the category.

Line two is the probability of of that outcome for that group.

Line three is the product of line one and two. It is summed at the end.

Line four is line three divided by the sum of line three. It gives us what’s called the “posterior probabilities”.

in Excel-

0.014285714	0.985714286

0.92	        0.02

0.013142857	0.019714286	0.032857143

0.4	        0.6

Using formulas:

=1/70	=69/70

=0.92	=0.02

=A1*A2	=B1*B2	=SUM(A3:B3)

=A3/C3	=B3/C3

So there is a .4 or 40% chance of having the allergy given that he had the allergic reaction.

The benefit of this method is that one doesn’t need a Venn Diagram to solve it.