Probability homework help

Question

about independent events E and F in a sample space S, but assume that Pr[E]=0.45 and Pr[F]=0.3.
Compute the following conditional probabilities:

(1) Pr[E′|F]


(2) Pr[E|F′]

Answer 1

If E and F are independent, then E ∩ F = E x F. 

 

P[E'|F] = 1 - P[E|F]

           = 1 - (P[E∩F]/P[F])

           = 1 - ((P[E]xP[F])/P[F])

 

 

 

 

 

 

 

Answer 2

Since E and F are independent, the probabilities of E and E' are invariant under whether F happened or not.

 

(1)  Pr(E'|F) = Pr(E') = 1 - Pr(E) = 1 - 0.45 = 0.55

 

(2)  Pr(E|F') = Pr(E) = 0.45