Question

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

Answer 1

`27/256~=10.55%`

Explanation:

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%`