How to calculate probability?

colerelm

New member
Joined
Oct 24, 2011
Messages
33
Can anyone help me figure out how to get started on this problem from my assignment? I'm not asking for the answers, rather I'd like to know what steps should be taken to solve the problem. Any help would be appreciated, thanks.

probs.jpg
 
Can anyone help me figure out how to get started on this problem from my assignment? I'm not asking for the answers, rather I'd like to know what steps should be taken to solve the problem. Any help would be appreciated, thanks.

View attachment 2374

I'll give you a hint for (a). You want P(~Y). It may help to ask yourself, what is the probability that I will choose ~Y from the two Z groups. So you must find the marginal distribution for ~Y for both Z and ~Z as it occurs in both groups. For Z, P(~Y) = 0.36 (do you see how I got that?), yet P(Z) = 0.60 (again, do you see how I got that?). Thus, P(~Y) for the Z group is (0.36)*(0.60) = 0.216.

Now try and find P(~Y) for the ~Z group. Then what do you think you do with these two amounts?
 
I'll give you a hint for (a). You want P(~Y). It may help to ask yourself, what is the probability that I will choose ~Y from the two Z groups. So you must find the marginal distribution for ~Y for both Z and ~Z as it occurs in both groups. For Z, P(~Y) = 0.36 (do you see how I got that?), yet P(Z) = 0.60 (again, do you see how I got that?). Thus, P(~Y) for the Z group is (0.36)*(0.60) = 0.216.

Now try and find P(~Y) for the ~Z group. Then what do you think you do with these two amounts?

Alright, thanks. I was able to figure it out with that info but I guess I'm stuck on part B now. I have a formula written down in my notes but I'm not sure if it's correct, can anyone confirm it?

P(x|~y) = [P(x)P(~y|x)]/P(~y)]

I've solved for P(x) but how do I calculate P(~y|x)?

Thanks again
 
That is a standard formula obtained from: P(AB)=P(A|B)P(B) = P(B|A)P(A) = P(BA).

So, P(~Y|X) = [P(X|~Y)P(~Y)]/P(X), of course you need that P(X)=/=0.
 
Top