Respuesta :
We're going to solve this problem using the standard ratio between good outcomes and all possible cases.
With the first draw, we have 52 possible outcomes (all the 52 cards could be drawn) and 13 good outcomes, since any of the 13 spade cards will be fine. So, the probability of drawing a spade is
[tex] \frac{13}{52} = \frac{1}{4} [/tex]
As for the second draw, we have 51 possible outcomes, since we're not replacing the first draw. Now, there are 26 black cards in the deck at the beginning, since we have 13 spades and 13 clubs. But we are assuming that the first draw was a spade, so we're left with 25 black cards: 12 spades and 13 clubs. So, the probability of drawing a black card is
[tex] \frac{25}{51} [/tex]
When you want two events to happen one after the other, you simply have to multiply their individual probability, so the answer is
[tex] \frac{1}{4}\cdot \frac{25}{51} = \frac{25}{204} [/tex]
