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I'm trying to figure out the probability of a 3rd failure occurring on the 5th attempt of doing something. Let's just call the probability of success of failure P(S) or P(F), I won't put numbers as I want to actually learn.

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HINTS:

  1. Can you imagine a sequence of successes and failures which would involve the 3rd failure occurring on the 5th attempt. What is the probability of this sequence?
  2. What is the probability of another sequence involving the 3rd failure occurring on the 5th attempt?
  3. How many sequences are there involving the 3rd failure occurring on the 5th attempt? (You could count them as it is certainly in single figures, or you might find an expression)
  4. How do you combine the probabilities of the different sequences?
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    Thank you for the help! This definitely means I need some help from my prof. Your patience was great.2011-03-01
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See Negative Binomial Distribution (the section "Alternative formulations").