Final answer:
The probability of being dealt an ace is 1/13; the probability of being dealt an ace or a king is 2/13; and the probability of being dealt two consecutive aces is 1/221.
Step-by-step explanation:
Firstly, there are 4 aces in a standard 52-card deck. The probability of being dealt an ace is 4 out of 52, which simplifies to 1/13, or approximately 7.69%. Next, there are also 4 kings in the deck, so for the probability of being dealt an ace or a king, we have 4 aces plus 4 kings, giving 8 favorable outcomes. The probability is 8 out of 52, which simplifies to 2/13 or roughly 15.38%. Finally, for the probability of being dealt an ace and then another ace, after the first ace is dealt, there are now 51 cards left and only 3 aces left. The probability is the multiplication of the probabilities of both events: (4/52) * (3/51), which simplifies to 1/221, or about 0.45%.
Step-by-Step Probability Calculations
For a single ace: Probability = Number of aces / Total number of cards = 4/52 = 1/13.
For an ace or a king: Probability = (Number of aces + Number of kings) / Total number of cards = (4 + 4)/52 = 2/13.
For two consecutive aces: Probability = (Number of aces / Total number of cards) * (Number of aces remaining / Total number of cards remaining) = (4/52) * (3/51).