Final answer:
The probability that the first card is a heart is 1/4. The probability that the second card is a club, given that the first card was a heart, is 13/51. The probability that the first card is a heart and the second card is a club is 1/12.
Step-by-step explanation:
To calculate the probability for each part of the question, we need to consider the total number of cards in the deck and the number of favorable outcomes for each event.
(a) Probability that the first card is a heart:
- There are 13 hearts in a standard deck of 52 cards, so the number of favorable outcomes is 13.
- The total number of cards in the deck is 52.
- Therefore, the probability is 13/52, which simplifies to 1/4.
(b) Probability that the second card is a club, given that the first card was a heart:
- After drawing the first card, there are 51 cards remaining in the deck.
- There are 13 clubs remaining in the deck.
- Therefore, the probability is 13/51.
(c) Probability that the first card is a heart and the second card is a club:
- Using the same reasoning as in part (a), the probability of drawing a heart first is 1/4.
- After drawing the first card, there are 51 cards remaining in the deck.
- There are 13 clubs remaining in the deck.
- Therefore, the probability is (1/4) * (13/51), which simplifies to 1/12.