What is the posterior probability of S1 given that the research predicts S1?
A)0 18
B)0 44
C)0 57
D)0 65
E)0 82

Question

What is the posterior probability of S1 given that the research predicts S1?
A)0 18 
B)0 44 
C)0 57 
D)0 65 
E)0 82

Quizplus · Accepted Answer

Based on Bayes' theorem, the posterior probability of an event A given event B is equal to (P(B|A)*P(A))/P(B). In this case, S1 is event A and the research predicting S1 is event B. From the table, we can see that P(S1) is 0.25, P(R|S1) is 0.9, and P(R|S2) is 0.3. Thus, using the formula, we get: P(S1|R) = (P(R|S1)*P(S1))/P(R) = (0.9*0.25)/(0.9*0.25 + 0.3*0.75) = 0.82. Therefore, the best choice is E.

What Is the Posterior Probability of S1 Given That the Research