Final answer:
To find P(T > 0.1) without using calculus, you can apply the count-time duality concept. In a Poisson process, the time elapsed between events follows an exponential distribution. Using the rate parameter of the exponential distribution, you can calculate the desired probability. In this case, P(T > 0.1) ≈ 0.1353.
Step-by-step explanation:
To find P(T > 0.1), we first need to understand the concept of a Poisson process and the count-time duality. In a Poisson process, events occur randomly and independently over a continuous time interval. The rate at which events occur is constant. The count-time duality states that the number of events occurring in a fixed time interval follows a Poisson distribution, and the time elapsed between events follows an exponential distribution.
In this case, T represents the time at which the 3rd email arrives. Since emails arrive in an inbox according to a Poisson process with a rate of 20 emails per hour, the time between emails follows an exponential distribution with a rate parameter of 20.
To find P(T > 0.1), we can use the property of the exponential distribution that states P(X > x) = e^(-λx), where λ is the rate parameter. In this case, λ = 20, and x = 0.1. Plugging in these values, we get P(T > 0.1) = e^(-20*0.1) = e^(-2) ≈ 0.1353.