I have a question regarding (a homework ) assignment. I've done some research but I couldn't get clear I were on the right track:
$8$ people want to decide who is the designated driver. They each draw a marble in turns without putting it back. One is red, the person who draws that is the designated driver.
$X$ is the amount of drawings needed to conclude a designated driver.
I assumed this is a hypergeometric experiment, but it is no where covert in the material available to us. That made me question if there is another way of doing it. Furthermore, I tought that each individual drawing could be seen as a seperate binomial experiment. We are asked to calculate $E(X)$, $\operatorname{Var}(X)$ and $P(X\geq 3)$. $E(X)$ could then be calculated by $E(X)=np_1 + np_2 + np_3 ... np_8$ and $\operatorname{Var}(X)$ the same way (the sum of each variance).
What is the correct way to approach this?
Sorry if I messed up some terms, because english isn't my native language and the course is given in dutch.