Final answer:
a) The probability that both cards are red is 325/1326. b) The probability that the first card is an ace and the second card is either a ten, jack, queen, or king is 16/663. c) If the card was returned to the deck before selecting the second card, the probabilities would remain the same as in the initial scenario.
Step-by-step explanation:
a) To find the probability that both cards are red, we need to determine the number of red cards and the total number of possible cards.
There are 26 red cards (13 hearts and 13 diamonds) and a total of 52 cards in the deck. Since we are selecting the cards without replacement, the number of possible outcomes decreases after each card is selected.
Therefore, the probability of selecting both cards as red is:
P(both cards are red) = (Number of red cards / Total number of cards) x (Number of red cards - 1 / Total number of cards - 1)
= (26/52) x (25/51) = 325/1326
b) To find the probability that the first card is an ace and the second card is either a ten, jack, queen, or king, we need to determine the number of desired outcomes and the total number of possible outcomes.
There are 4 aces and 16 cards (10, J, Q, and K) in the deck that satisfy the condition. The probability can be calculated as:
P(ace on 1st card and 10/J/Q/K on 2nd card) = (Number of aces / Total number of cards) x (Number of 10/J/Q/K cards / Total number of cards - 1)
= (4/52) x (16/51) = 16/663
c) If we were returning the card to the deck before selecting the second card, the probability would remain the same as the initial probabilities calculated in (a) and (b).