catch fish problem There are 20 fish in a lake, among them 5 are trouts. What is the probability that a fisherman have to catch more than 6 fish in order to obtain 3 trouts? Assume he keeps every fish he caught. 
How do I solve the above problem? Should I define the number of trouts cauth as random variable X or the number of fish caught instead?
Much thanks!
 A: You should first make yourself clear, what is your probability space. The define a proper measure on it. Or you could modell it, you have an urn with 20 balls in it, 5 of them black. You take n balls after each other, and dont put them back. The resultion distribution would be called, hypergeometric distribution. I would define the number of trouts caught :)
And also define the set you want to measure. he has caught 6 fish, but has strictly less than 3 trouts, so how many trouts could he have caught...
A: Hint: If I understand the question correctly, you need that at most $2$ out of the first $6$ fishes will be trouts. The number $X$ of trouts in the first $6$ catches is a hypergeometric random variable with parameters $N=20$ (population size), $k=5$ (number of successes in the population), $n=6$ (sample size). You need the probability $$P(X\le 2)$$ 
A: HINT: There are $\binom{15}6$ sets of $6$ fish that contain no trout. (Why?) 


*

*How many sets of $6$ fish contain exactly $1$ trout?  

*How many contain exactly $2$ trout?  

*How many contain at most $2$ trout?  

*How many possible sets of $6$ fish are there?  

*What is the probability that he catches at most $2$ trout in his $6$ fish?

