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Cards are lifted one at a time from a shuffled pack of 52, the first one NOT being put back. The first card lifted turns out to be a queen. What is the probability that the next card lifted is also a queen?

Competition practiceProbability & Permutation
  • A1/13
  • B3/52
  • C4/51
  • D1/17

Step-by-Step Solution

The first queen is already out of the pack, so 51 cards remain and only 3 of them are queens: 3/51 = 1/17. Trap 1/13 = 4/52 forgets both changes and re-uses the fresh-pack figure. Trap 3/52 remembers that a queen has gone but still divides by the full 52. Trap 4/51 does the reverse — it shrinks the pack to 51 but still counts 4 queens in it.
Answer: D) 1/17

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