Finding the probability of getting no successes in a Geometric DistributionIn Geometric Distribution, I am getting the probability for doing x number of trials and get my first success with each trial of probability p.So suppose I want to find what's the probability of doing 30 trials and get my first success on the 30th trial, I do this: P ( X = 30 ) = ( 1 − p ) 30 − 1 pNow, then if I want to find the probability for not getting a single success at all even after doing 30 trials on this same distribution, what should I do? The parameters of the Geometric Distribution doesn't seem to let me find this.I thought of using like 1 minus the CDF of 30 trials of the geometric distribution but I am not sure if it would be accurate.

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Finding the probability of getting no successes in a Geometric DistributionIn Geometric Distribution, I am getting the probability for doing x number of trials and get my first success with each trial of probability p.So suppose I want to find what&#039;s the probability of doing 30 trials and get my first success on the 30th trial, I do this:  P  (  X  =  30  )  =  (  1  −  p      )          30      −      1        pNow, then if I want to find the probability for not getting a single success at all even after doing 30 trials on this same distribution, what should I do? The parameters of the Geometric Distribution doesn&#039;t seem to let me find this.I thought of using like 1 minus the CDF of 30 trials of the geometric distribution but I am not sure if it would be accurate.

vibrerentb · Accepted Answer

Step 1How did you arrive at   P  (  X  =  30  )  =  (  1  −  p      )          30      −      1        p? Usually this is derived by arguing that to have the first success in the 30-th trial you need to have 29 trials without success and then one trial with success, which makes   (  1  −  p      )          29        p.Step 2But that argument already contains the answer to your question, namely, since the probability of not getting a success in one trial is   1  −  p, the probability of not getting a success in 29 trials is   (  1  −  p      )          29      , and analogously the probability of not getting a success in 30 trials is   (  1  −  p      )          30      . So you took the second step before the first.

Find what's the probability of doing 30 trials and get my first success on the 30th trial, I do this: P(X=30)=(1-p)^{30-1}p

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