Final answer:
The probability of drawing a face card given that a black card is drawn from a standard deck of 52 playing cards is 3/13 or approximately 0.2308.
Step-by-step explanation:
The student has asked for the probability of drawing a face card from a standard deck given that a black card is drawn. To find this probability, we first need to consider the number of black face cards in a standard deck of 52 playing cards. In a standard deck, there are two black suits: clubs and spades. Each suit has three face cards (jack, queen, and king), so there are a total of 6 black face cards.
Since we know a black card is drawn, we limit our sample space to the 26 black cards. Out of these, 6 are face cards. Thus, the probability of drawing a face card given that we've drawn a black card is 6 divided by 26, which simplifies to 3/13 or approximately 0.2308. This is a conditional probability since the event is conditioned on the fact that a black card is drawn.