High School Precalc Probability problem?

Question

If two cards are selected form a standard deck of playing cards (one after nother without replacement), what is the probability that a heart then a black face card will be chosen?

can anyone please teach me how to do this problem and also give me the answer?

Answer 1

There are 13 hearts in a deck of 52 cards. So the chances of a heart being drawn first is 13/52 or 1/4. If we don't replace that card, we now have 51 cards remaining. Of those 51, if we discount Aces, which aren't really face cards, there are 6 black face cards: 2 Jacks, 2 Queens and 2 Kings. Then there are 6 out of the 51 cards which are black face cards. The probably that one event will follow another then is simply the product of their individual probabilities:

1/4 x 6/51 = 6/204 = 3/102 = 1/34 ≈ 2.94%.

If we count the Aces as face cards, then there are 8 out of the 51 which are black face cards, and the probability above becomes:

1/4 x 8/51 = 2/51 ≈ 3.92%.

Answer 2

(1/4)*(6/51) = 3/102

I take "standard deck" to mean 52 cards (no jokers).
The first card will be a heart one fourth of the time. There are then 6 face cards in the remaining 51 cards.

So of the one fourth of the times that the first card actually IS a heart, 6/51 of those times the second card will be a black jack, queen or king.