SOLUTION: P(E1)=0.25, P(E2)= 0.75, P(F|E1)=0.05, p(F|E2)=0.12 P(E2|F)= A. 0.188 B. 0.878 C. 0.060 D. 0.370

Algebra ->  Probability-and-statistics -> SOLUTION: P(E1)=0.25, P(E2)= 0.75, P(F|E1)=0.05, p(F|E2)=0.12 P(E2|F)= A. 0.188 B. 0.878 C. 0.060 D. 0.370      Log On


   

Question 86397: P(E1)=0.25, P(E2)= 0.75, P(F|E1)=0.05, p(F|E2)=0.12
P(E2|F)=


A. 0.188
B. 0.878
C. 0.060
D. 0.370
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
P(E1)=0.25
P(E2)= 0.75
P(F|E1)=0.05
p(F|E2)=0.12
Find P(E2|F)=
----------------
P(E2|F) = [P(E2 and F)]/P(F)
=[P(F|E2)*P(E2)]/P(F)
You know P(F|E2) and you know P(E2)
Need to find P(F)
-----------
P(F) = P(F and E1) + P(F and E2)
= P(F|E1)*P(E1) + P(F|E2)*P(E2)
You know all of these.
---------------
Substituting you get:
P(E2|F) = (0.12*0.75)/[0.05*0.25+0.12*0.75]
= 0.09/0.1025
= 0.878
=============
Cheers,
Stan H.