In a standard deck of 52 playing cards, without replacement, what is the probability that the first card drawn is a red ace and the second card drawn is a face card or an ace?

In a standard deck of 52 playing cards, without replacement, what is the probability that the first card drawn is a red ace and the second card drawn is a face card or an ace?

• A. 5/442
• B. 1/26
• C. 15/51
• D. 3/50

Answer: (A)

This question tests conditional probability with drawing without replacement. Start by focusing on the first draw: the chance of getting a red ace is 2 out of 52, which is 1/26. Once that red ace is gone, 51 cards remain, and among them there are 12 face cards plus 3 aces left, totaling 15 favorable second-card outcomes. So the second draw being a face card or an ace has probability 15/51. Multiply the two steps: (1/26) × (15/51) = 15/1326 = 5/442. The joint probability thus is 5/442.

This question tests conditional probability with drawing without replacement. Start by focusing on the first draw: the chance of getting a red ace is 2 out of 52, which is 1/26. Once that red ace is gone, 51 cards remain, and among them there are 12 face cards plus 3 aces left, totaling 15 favorable second-card outcomes. So the second draw being a face card or an ace has probability 15/51. Multiply the two steps: (1/26) × (15/51) = 15/1326 = 5/442. The joint probability thus is 5/442.