Consider of drawing one card from a deck of $52$. Prove that the events of a spade being drawn and an ace being drawn are independent events.
Let $A$ be the event that a spade is drawn and let $B$ be the event that an ace is drawn.
Then, $\text P(A) = 4/52 = 1/13$ and $\text P(B) = 4/52 = 1/13$.
How can I calculate $\text P(A\cap B)$? And how can I prove that these events are independent since the question specifically asked to prove that they are independent?