Part 1 (Entry #10) explained how to use this concept with independent filters that all had about the same success rate. This part will show how to do so with filters that have different success rates from each other. Since the setup math is more involved, fewer filters are used in the example. I'm using 3 filters total. Their success rates are: 80/20, 75/25, and 70/30

   

Step 1 set up a "truth table" 1 column for each filter and 2^filters rows (2^3 = 8), thus...

                                                                                                    

filter 1	filter 2	filter 3
80/20	75/25	70/30
pass	pass	pass
pass	pass	fail
pass	fail	pass
pass	fail	fail
fail	pass	pass
fail	pass	fail
fail	fail	pass
fail	fail	fail

 

step 2: substitute the "pass" and "fail" spaces with your pass/fail ratios...

then multiply across (I added a column for "totals")

filter 1	filter 2	filter 3
80/20	75/25	70/30
80%	75%	70%	42.0%
80%	75%	30%	18.0%
80%	25%	70%	14.0%
80%	25%	30%	6.0%
20%	75%	70%	10.5%
20%	75%	30%	4.5%
20%	25%	70%	3.5%
20%	25%	30%	1.5%

Now you have all eight possible outcomes, and their expected rate of occurence.

What happens if you decide you want to drop a filter?

Here's how. Dropping filter 3 and marking out all redundancies in cols 1 and 2 gives this table.

Two filters gives only four possible outcomes. You would call the third filter a "don't care" condition. 

filter 1	filter 2	filter 3
80/20	75/25	70/30
80%	75%		60.0%
80%	25%		20.0%
20%	75%		15.0%
20%	25%		5.0%