I need some help with this question regarding Hypergeometric distribution.
We mix in an urn 15 coins. 5 coins of 1 pound, 5 coins of 50 pens and 5 coins of 20 pens.
we choose randomly and without replacement 4 coins. X is defined as the number of coins of 1 pound.
a. what is the probability function of X, calculate E(X) and Var(X)
b. what is the probability to have maximum 2 coins of 20 pens ?
c. what is the probability to have at least 1 coin of 50 pens ?
I started with:
P(X=k)=((5 over k)*(10over 4-k)) / (15 over 4)
Var(X)=[4*5*(15-4)*(15-5)] / [225*(15-1)]
is it correct ? how to solve b and c ? a hint would be appreciated !