two events

Question

For two? events, M and? N, ?P(M)=0.4, ?P(N|M)=0.2?, and ?P(N|M')=0.7. Find ?P(M'?|N?).

Answer 1

P(N/M) =  p(n∩M)/p(M) = p(N∩M)/.4 = .2 or cross multiply to get p(N∩M)= .08

 

P(N/M') = p(N∩M')/p(m') = p(N∩M')/.6 = .7 or p(N∩M') = .42

 

P(M'/N) = P(M'∩N)/P(n) = .42/p(N)

 

So looking at the tree diagram from the other problem, you have 4 possibilities,

 

P( M and N) = .08

P (M' and N)= .42

P (M and N') =?

P( M' andN')=?

 

So P(N) = .5........08+.42

 

So your answer is .42/.5 = .84

 

Hope this made some sense to you.