 # Applying Bayes' Rule

I’m having difficulty doing a homework problem involving Bayes’ rule.

The formula to be used is:

P(A|B) = P(A)*P(B\A) / (P(Ai)*P(B|Ai) (The formula can be better seen at the bottom of thispage)

My problem lies in the fact that after many tries, I do not know my variables’ values from this set of probabilities:

P(F|Small) = .3 P(U|Small) = .7
P(F|Medium) = .6 P(U|Medium) = .4
P(F|Large) = .8 P(U|Large) = .2

With F = Favorable and U = Unfavorable

Just can’t figure out what values to fill in the formula to get the answers which are :

.17 .45
.68 .51
.15 .04

If someone could show the steps to get one of the answers I’m sure I can figure out how to do the rest. Thanks in advance!

What’s the actual question?

I can reproduce the answers that you’ve given, assuming that, reading down the columns, they are: P(Small|F), P(Medium|F), P(Large|F), P(Small|U), P(Medium|U), P(Large|U).
I’d suggest you look at the question again and see whether there’s any additional information given to you.

That is exactly my question, how did you reproduce those answers. The question is actually long and tedious (computing EVSI) but not necessary to the question at hand. I cannot figure out how to “plug” in the correct sequence of variables into the formula to achieve the given answers. Could you show step by step how you plugged in the answers.

i.e. Using the formula, how do you get .17 for P(F|S) = .3?

Thanks.

Are you sure that the question doesn’t give some information about the relative probabilities of Small, Medium and Large events?

Oops:

Small: .3
Medium: .6
Large: .1

Exactly. You need that information. I fiddled around for a few minutes with the correct answers that you provided and realised that they implied probabilities of small, medium and large events of 30%, 60% and 10% respectively.

You shouldn’t have too much difficulty applying the formula now.

Actually, I just figured it out after reading your question to my post. It all makes sense now, I was missing information…no wonder…Thanks a lot lol.

Uh oh. Now I have to figure out the probability of Favorable and Unfavorable.