Bayes Formula

Anyone think this will show up on the test? I think I understand these, but then get so confused setting them up…

i think this was tested in L1 lol…doubt it will show up in L3 unless in the capacity of describing a rational economic man…someone who updates his/her beliefs according to bayes rule

i was pretty pissed when i saw this in L3, because it is nothing more than tedious minutiae.

idk how they can test something like this at L1 and then again at L3. i think of a million other things, which never show up in the curriculum at all, that are more important than this crap.

Yep. They also better not test Type I & Type II errors. I put those in the same box as Bayes formula…

if they do ask this, it would be one of the easier questions they asked. :slight_smile:

I do not believe this is part of an LOS…any disagreers?

I don’t think the LOS cover the forumla. Discuss does not mean calculate.

Addtionally, I think that the conditional probability of us misinterpreting the LOS & the CFA deciding to test on this material is very low.

50% of Level III candidates pass the test with a question on Bayes formula and only 10% of all candidates actually know how to calculate Bayes formula and all that know it also pass, What is the chance you (assuming you don’t know bayes formula) are one of the candidates which passes?

OK I can’t help it.

I’m going to pose a q using Bayes formula:

Manufacturer A claims he has a test to detect a tire that will fail in 1 year which works accurately 95% of the time.

He neglects to mention that tires that do not fail in 1 year are also detected as bad by his test 15% of the time.

In a batch 10% of the tires are defective and will fail in 1 year .

A particular tire has just failed the test.

What is the probability that it is actually defective



Hint: draw a tree graph , with outcomes as nodes and probabilities as leaves.

outcomes are :

tire is defective or not defective.

test detects the tire as defective or does not detect the tire as defective.

I’ll give another hint after I see some more answers. I am not saying Fin is wrong


Tire is defective 0.10 Test says defective 0.95 Test says not defective 0.05 Tire is not defective 0.90 Test says defective 0.15 Not defective 0.85 P(Actually defective ) = 0.10 * .95 / (.1*.95 + .9*.15) = .413?

I must be doing something horribly wrong because I got 41.3%.

aaron and cpk are correct.

Man, I missed the 2nd 15% probabiliy. I assumed the test was 95% accurate across the board…

This was a good review, I haven’t looked at Bayes in about 2 months. I had the right equation, just didn’t have the right P(B). I’ll have to draw it out like CPK next time.

Ninja down!

could n’t get :frowning:

The end result is known ( tire is tested defective ). Now follow the two paths ( probability weighted ). 1st path is a true positive . 2nd one is false positive.

( this 2nd one seems confusing , but isn’t . 0.9 is probability that tire is not defective across all batches ( independently , 0.15 is the independent probability of the test showing a false positive . the combined probability is 0.9*0.15 )

1st path : true positive : 0.1 * 0.95

2nd path : false positive : 0.9 * 0.15

Add the two together to come up with the total probability of the test detecting a positive.

Out of these the weight given to the first path ( because the test succeeded and because we’re estimating the test is right ) is :

1st path prob / (1st path prob + 2nd path prob ) , which gives the right answer .

So improbably enough a 95% accurate test gives a confidence of only 41.3 % in a positive result.