If P(E and F)=.392, P(E/F)=.56 and P(F/E)=.7, then find the following

Question

A) P(E)=

B)P(F)=

C)P(E or F)=

Answer 1

Hello Sarah,

Recall the general multiplication rule:

P(A and B) = P(A)P(B|A).

Note that since P(A and B) = P(B and A), this may also be written as P(A and B) = P(B)P(A|B).

Part a) Using the general multiplication rule, we have

P(E and F) = P(E)P(F|E)

.392 = P(E)(.7)

Solve for P(E) to obtain

P(E) = .56

Part b) P(E and F) = P(F)P(E|F)

.392 = P(F)(.56), so

P(F) = .7

Part c) To find P(E or F), use the general addition rule:

P(E or F) = P(E) + P(F) - P(E and F)

I will let you substitute in the appropriate values and get the final result.

Hope that helps! Let me know if you need any more assistance.

William