Consider Bernoulli trials with success probability p=1/4. What is the probability that the first success occurs in the fourth trial?

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Answer 1 · 2017-02-23T09:44:02

#27/256~=10.55%#

We can approach this by first seeing that with the probability of success being #1/4#, the probability of failure is #3/4#.

Next we need to remember that each trial is independent. We have a specific set of outcomes that we're solving for:

(Fail, Fail, Fail, Success)

and with the related probabilities of each:

#(3/4, 3/4, 3/4, 1/4)#

we can multiply each probability to find an overall probability of the first success on the 4th attempt:

#(3/4xx 3/4xx3/4xx 1/4)=27/256~=10.55%#