Question

How do you find the probability of no successes when `n` independent Bernoulli trials are carried out with probability of success `p`?

Answer 1

`(1-p)^n`.

Explanation:

The probability of failure is `(1-p)` as the probability of success is `p` and there is only two outcomes in a Bernoulli trial.

If there were two trials, both resulting in failure, the probability would be `(1-p)*(1-p)` or `(1-p)^2` as the events are independent.

If there were `n` trials, the probability would be `(1-p)*(1-p)*...*(1-p)` with a `1-p` for each of the `n` events. So the probability would be `(1-p)^n`.