<s>[INST] Probability of cards drawn from a deck 
The cards are drawn from a well shuffled deck of 52 cards one after
  the other without replacement. The probability of first card being a
  spade and the second a black king is ?

Here, is my approach,
Upon first draw we got a black spade king
$$P(\text{first card is spade}) = \frac{13}{52}$$
$$ P(\text{second black king}) = \frac{1}{51} $$
Upon first draw we don't get a black spade king
$$P(\text{first card is spade}) = \frac{13}{52}$$
$$ P(\text{second black king}) = \frac{2}{51} $$
Now, the total probability,
$$P= \frac{13}{52} \frac{1}{51} + \frac{13}{52} \frac{2}{51} = \frac{39}{2652}$$
But the actual answer is $\frac{25}{2652}$
 [/INST] Upon first draw we got a black spade king
$$P(\text{first card is $K \spadesuit$}) = \frac{1}{52}$$
$$ P(\text{second black king i.e $K\clubsuit$}) = \frac{1}{51} $$
Upon first draw we don't get a black spade king
$$P(\text{first card is $\spadesuit$ but not $K\spadesuit$}) = \frac{12}{52}$$
$$ P(\text{second black $K$}) = \frac{2}{51} $$
Now, the total probability,
$$P= \frac{1}{52} \frac{1}{51} + \frac{12}{52} \frac{2}{51} = \frac{25}{2652}$$
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