Final answer:
To calculate the probability of drawing a four first and a heart second from a shuffled deck with replacement, you multiply the probability of each independent event. The combined probability of these two events is 1/52.
Step-by-step explanation:
The probability of drawing a four the first time and a heart the second time from a 52 card deck involves calculating the probability of each event separately and then multiplying them, since the events are independent. There are 4 fours in a deck, so the probability of drawing a four is 4/52 or 1/13. Since the card is replaced, the probability of drawing a heart the second time is the number of hearts in the deck (13) divided by the total number of cards (52), which is also 1/4. To find the combined probability of both events occurring, you multiply the individual probabilities: (1/13) × (1/4) = 1/52.