A store opens at $t =0$ and potential customers arrive in a Poisson manner at an average arrival rate of $λ$ potential customers per hour. As long as the store is open, and independently of all other events, each particular potential customer becomes an actual customer with probability $p$. The store closes as soon as ten actual customers have arrived.
Considering only customers arriving between $t =0$ and the closing of the store, what is the probability that no two actual customers arrive within $τ$ time units of each other?
Thanks! Could you give me idea or answer? Why downvote? The given answer is a little werid that I could not understand...