I have 3 different exercises and I am getting confused.If it is Poison or Bernoulli or e. I have seen and I know each and read, but I am not so clever to get it.I mean i can't detect the exercise what it is. Can you share me trick to help me get it? I have used Bernoulli in cases that it needs Poisson and the opposite. If you can help me not solve it but explain me why is Bernoulli from where you understand it, I will be grateful. first exercise
There is a race of markets to sell their cornflakes.A company calls random numbers with purpose to promote their cornflakes to customers. We have as sure that this company has already 20% of all markers. What is the possibility one phone caller person(mean that work in this company) that calls customers to need more than 3 calls until she will succeed someone who is not a customer? My answer:I don't know what typology to use
second exercise
One internet company service 4 servers,and the two of them are "hosting" the database and the other 2 our doing the software. The possibility we will have damage in a server the next year is $1\%$. We take as granted that the possibility of to appear damage in every server is independently each one. If the internet company are working it must be at least 1 server that will have the database and one server that will doing the software. What is the possibility the company will work normally and the next year?
The first exercise seems to be Bernoulli since there are only two events: A = the staff needs more than 3 calls until she will reach who is not already a customer B = the staff reach who is not already a customer within the first three calls $P(A) = 1 - P(B)$
$\begin{align} P(B) = &P(\text{the first call was non-customer}) \\ &+ P(\text{the first call was customer, the second call was not non-customer}) \\ &+ P(\text{the first and second call was customer and the third call was not a customer})\\ =& \frac{8}{10} + \frac{2}{10} \cdot \frac{8}{10} + \frac{2}{10} \cdot\frac{2}{10} \cdot\frac{8}{10} = \frac{992}{1000}\\ \end{align} $
$P(A) = 1= P(B) = \frac{8}{1000}$
Applying same logic as the first question, the second question has two events: the company functions normally and otherwise. Therefore, it has Bernoulli distribution.