Given Pr(a)= 0.9, Pr(C|A)= 0.78 and Pr(D|B) = 0.38. find
a. (A|C) =
b. (A|D) =
c. (B|C) =
d. (B|D) =
To find the values of (A|C), (A|D), (B|C), and (B|D), we will need to use Bayes' Theorem. Bayes' Theorem states that for any two events A and B:
Pr(A|B) = (Pr(B|A) * Pr(A)) / Pr(B)
a. (A|C):
Pr(A|C) = (Pr(C|A) * Pr(A)) / Pr(C)
Here, we are given that Pr(C|A) = 0.78 and Pr(A) = 0.9.
To find Pr(C), we can use the Law of Total Probability:
Pr(C) = Pr(C|A) * Pr(A) + Pr(C|Ac) * Pr(Ac)
Since we don't have Pr(C|Ac), we cannot directly find Pr(C). Therefore, we cannot determine (A|C) with the information provided.
b. (A|D):
Pr(A|D) = (Pr(D|A) * Pr(A)) / Pr(D)
Since we don't have Pr(D|A), we cannot directly find Pr(A|D). Therefore, we cannot determine (A|D) with the information provided.
c. (B|C):
Pr(B|C) = (Pr(C|B) * Pr(B)) / Pr(C)
Here, we are given Pr(C|B), which is not directly related to Pr(B|C). Therefore, we cannot determine (B|C) with the information provided.
d. (B|D):
Pr(B|D) = (Pr(D|B) * Pr(B)) / Pr(D)
We are given Pr(D|B) = 0.38 and Pr(D), but we don't have Pr(B). Therefore, we cannot determine (B|D) with the information provided.
In summary, we cannot determine the values of (A|C), (A|D), (B|C), and (B|D) with the given information.