Final answer:
The probability that the first card drawn is a heart and the second card drawn is black, without replacement, is 0.127 when rounded to three decimal places.
Step-by-step explanation:
The question asks for the probability that the first card drawn from a standard deck is a heart and the second card drawn is black, without replacement. A standard deck has 52 cards, with 13 cards in each of the four suits (hearts, spades, clubs, and diamonds). Since hearts are red and spades and clubs are black, we can calculate the probability of this two-step event.
For the first card to be a heart, the probability is 13 hearts/52 total cards which simplifies to 1/4 or 0.25. As we do not replace the first card, there are now 51 cards left in the deck. The probability that the second card is black (either spade or club) becomes 26 black cards/51 remaining cards, simplifying to 26/51. To find the combined probability of both events happening in sequence, we multiply the probabilities together:
Probability of first card being a heart and second card being black = (13/52) × (26/51) = 0.25 × 0.5098 = 0.1275 (rounded to three decimal places)
Thus, the answer is 0.127 when rounded to three decimal places.