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

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SUMMARY

The discussion centers on proving that the probability of event E occurring before event F, given that E and F are disjoint events, is expressed as P(E)/(P(E)+P(F)). The participants highlight the conditional probability approach and suggest using Bayes' Rule to analyze the situation. The key insight is recognizing that the experiment ceases once either event occurs, making it essential to evaluate the probabilities of both events occurring first.

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

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