Thread: Help Understanding Conditional Probability

I am in a finite mathematics class and have been given the following Pr[A|B] = 3/4 Pr[B|A] = 3/8 and Pr[A u B] = 1
I have been asked to find Pr[A] Pr[B] and Pr[A n B]
the book has provided the formula:

Pr[A|B] = Pr[A n B] Pr[B|A] = Pr[B n A]
Pr[B] Pr[A]

I am having difficulty understanding where to begin with this. Thanks.

Note that Pr[A u B] = Pr[A] + Pr[B] - Pr[A n B].

Originally Posted by batman

Note that Pr[A u B] = Pr[A] + Pr[b] - Pr[A n B].

Batman,
Thanks for the reply. Given Pr[A|B] = 3/4 Pr[B|A] = 3/8 and Pr[A u B] = 1. How do I arrive at Pr[A] or Pr[B]?

Originally Posted by mlynch18

I am in a finite mathematics class and have been given the following Pr[A|B] = 3/4 Pr[B|A] = 3/8 and Pr[A u B] = 1
I have been asked to find Pr[A] Pr[b] and Pr[A n B]
the book has provided the formula:

Pr[A|B] = Pr[A n B] Pr[B|A] = Pr[B n A]
Pr[b] Pr[A]

I am having difficulty understanding where to begin with this. Thanks.

.... (1)

.... (2)

Equate equations (1) and (2): .... (3)



Substitute from equations (3) and (1):

.

Solve for Pr(B). Hence solve for Pr(A) and .