Probability Proof: Showing P(E) Before F is P(E)/(P(E)+P(F))

[Kalinka35]

Homework Statement

Let E and F be disjoint events in an experiment's sample space. The trials of the experiment repeat until either event E or event F occurs. Show that the probability that E occurs before F is P(E)/(P(E)+P(F))

Homework Equations

The Attempt at a Solution

I tried viewing P(E before F) as a conditional probability along the lines of P(E | F hasn't occurred) and attempting to apply Bayes' Rule in some way but this doesn't seem correct and it hasn't really gotten me anywhere. I'm not sure really how to begin looking at it.

 

[Elucidus]

You are correct in that it is a conditional probability. Once one of the two events occur, the experiment stops. With E first it is successful, with F first, it is not.

Try P(E|E \cup F)[/tex]<br /> <br /> --Elucidus