Question

Let's say you own a website that sells a single product. Your product dashboard has provided the following metrics:

• The probability that a visitor will convert is .05 (we will assume that conversion is "iid", short for: independent and identically distributed).
• An average of 45 users visit the site every hour.

What is the probability that exactly 2 out of 10 randomly selected visitors will convert?

Starting now, what is the probability that you will have to wait more than 2 minutes until the next user visits?

Answer 1

1)

Let X denote the number of visitors that will convert. Then

Required probability =

2)

Let Y denote the time between two consecutive user visits (per minute). Then

Required probability =