Q:

Independence in card deck

Suppose you pick three cards, one at a time without replacement, from a
pack of 52 cards. Let Hi be the event that the ith card is hearts. 
How can i prove that H1 and H2 (first being a heart, and second being a heart) are independent or not

A:

They are dependent.  $H_1$ has probability $\dfrac{13}{52} = \dfrac14$ chance of being a heart.  If $H_1$ then $H_2$ has probability $\dfrac{12}{51}$, else $H_2$ has probability $\dfrac{13}{51}$.

