My problem question is:
Let $X$ be the number of spades in $7$ cards dealt from a well-shuffled deck of $52$ cards containing $13$ spades. Find $E[X]$
Now, I was thinking of using a hypergeometric distribution. However, after solving it I got my answer as $\frac{13}{4}$. However, the back of the book and this answer (Confusion about indicators) seem to point to the answer being $\frac{7}{4}$. I have rechecked my work many times and there are no errors. Why are these two numbers different?
You should still get $\frac{7}{4}$ using a hypergeometric distribution:
$$\sum_{k=1}^7 k \left(\matrix{13\\ k}\right)\left(\matrix{52-13\\ 7-k}\right)/ \left(\matrix{52\\ 7}\right) = 7/4. $$