I'm having trouble picking apart this summation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum[/tex][tex]^{inf}_{n=1}[/tex] P(E)*P(1-p)[tex]^{n-1}[/tex]; where p = P(E) + P(F)

I know I need to use the identity of a geometrical series when |r| < 1 : 1/(1-r)

I'm getting [tex]P(E)/(1-(P(E)+P(F))[/tex]

But I need to be getting P(E)/((P(E)+P(F));

The entire problem is

Let E & F be mutually exclusive events in the sample space of an experiment. Suppose that the exp is repeated until either event E or F occurs. What does the sample space of hte new super experiment look like? Show that the probability of event E before event F is P(E)/(P(E)+P(F)).

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# Summation of infinite series

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