Compute the following conditional probabilities

Question

about independent events A and B in a sample space S, but assume that Pr[A] = 0.25 and Pr[B] = 0.3.
Compute the following conditional probabilities:

(1) Pr[A | B] =

(2) Pr[B | A] =

Answer 1

Hello,

This problem is about conditional probability:

To find, we have a formula Pr(B | A)= Pr(AB)

                                                      Pr(A)

 

We know that Pr(A)=0.25, but what is Pr(AB)?

Since the events A and B are said to be independent we have that Pr(AB)=Pr(A)Pr(B).

 

Therefore, Pr(AB)=Pr(A)Pr(B)= 0.25*0.3=0.075

Now we return to Pr(B | A)= Pr(AB) = 0.075 =  0.3

                                         Pr(A)      0.25

 

 

Now for Pr(A | B) is very similar to this one. Can you figure it out? If you have any questions or would like more help please contact me.

 

Regards,

Manuel Rivera