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1.Customers arrive at a bank at a poisson rate. Suppose that two customers arrived during the first hour. What is the probability that

(A) both arrived during the first $20$ minutes?

(B) at least one arrived during the first 20 minutes?

(A) $N(60)=2$ within $(0,20)$. $(2/60)^{20}$. The answer is $\frac19$.

Though I know my answer isn’t it. I don’t what I am doing wrong. I want to see the steps to understand the question.

This is a self study question. At the time it drove me nuts

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It is known that for a poisson process, given that there are two arrivals in the first hour. Each arrival is independent and the arrival time is uniformly distributed. Hence, it should be

$$\left(\frac{20}{60} \right)^2=\frac19$$

Hint for the second part would be to consider the complement event and use similar computation as the first part.

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