Question on the application of the property of memorylessness of exponential distribution at example

Question

So I recently leant about exponential distribution and there got to know about its memorylessness. Then I attempted a question that went like this -

Q1) A site gets 3 visitors by a click every hour so μ = 20 minutes

a) Find the probability of getting a click in the first minute - ANS 0.05

b) If the site did not get a visit in the first 20 minutes, find the probability of getting a click in the 21st minute. - ANS 0.05

Here the memorylessness property of exponential distribution is applied and we see that both the q have the same probability.

Q2) Then I found another problem where we have to find the probability of a click happening in the 2nd minute the explanation was that the probability of not getting a click in the first minute and getting a click in the second minute this came out to be (.95)*(.05) essentially.

I am having trouble with the 2nd problem, isn't it the same as part b) of the 1st problem and so the probability should be 0.05 instead of the given answer due to the memorylessness of exponential distributions?

Answer 1

Why I asked for the exact wording is to clearly get the intention of the questions

• If you ask (regardless of what has happened in the past), what is the probability of a click in the 2nd minute, the answer is $0.05$ due to the memorylessness property.
• If you ask what is the probability that the first click occurs in the 2nd minute, the answer is $0.95*0.05$