So I'm currently a bit stuck on this question (see image below)
For part a), since $i = 1,2,\cdots,10$, the Bernoulli variable can correspond with the number of balls drawn. Hence, for each $i$, $P(X=1)$ can represent the scenario of a white ball being chosen and $P(X=0)$ for a black ball being chosen. However, I'm not sure how to find $p$ since this scenario doesn't involve replacement, so it varies for each $i$?
For part b), I'm assuming $i = 1,2,\cdots,17$ corresponds to the total number of white balls (whether it has been selected or not), however, in this case, I'm also not sure how to exactly calculate $p$, which would be needed for part c).
An explanation would be greatly appreciated, thank you!
Hint:
This is a hypergeometric distribution.
$$P(X=k)=\frac{{K \choose k}{N-K \choose n-k}}{N \choose n}$$
where
$$N \text{ is the number of balls in the population}$$
$$K \text{ is the number of white balls in the population}$$
$$n \text{ is the number of draws}$$
$$k \text{ is the observed number of white balls}$$
Use this to find the probability mass functions for $n=10$ and $n=17$ and use the fact that
$$E(X)=\sum_{i=1}^nx_ip_i$$