Compute probability at least one user uses feature

Q: Compute probability at least one user uses feature

This question evaluates understanding of basic probability concepts including independent Bernoulli trials, complementary probability, conditional probability, and conditional expectation.

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Problem

Assume there are $n$ users. Each user independently uses a certain feature with probability $p$ .

What is the probability that at least one user uses the feature?
What is the probability that a particular user (say user 1) used the feature given that at least one user used it ?
(Optional extension) What is the expected number of users who used the feature given that at least one user used it ?

Compute probability at least one user uses feature

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Compute probability at least one user uses feature

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