Multiple choice

Two cards are drawn at random from a standard deck of 52 playing cards without replacement. What is the probability that the first card is a Queen and the second card is a King? (a) 1/169 (b) 4/663 (c) 8/663 (d) 1/221 (e) 4/221

  1. C

  2. E

  3. D

  4. B

  5. A
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The probability of drawing a Queen first is 4/52, followed by a King with probability 4/51. Thus the required probability is (4/52)(4/51) = 4/663, which corresponds to choice (b).

AI explanation

Using the multiplication theorem for dependent events, the probability of the first card being a Queen is 4 divided by 52, or 1 divided by 13. Since the first card is not replaced, the probability of the second card being a King is 4 divided by 51. Multiplying these gives 1 divided by 13 times 4 divided by 51, which equals 4 divided by 663.

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