Probability · Class 11 · CBSE · Science Mathematics

Two cards are drawn successively without replacement from a standard deck of 52 cards. What is the probability that exactly one of the two cards is a…

Practice question from Probability (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-BEB0F5

Two cards are drawn successively without replacement from a standard deck of 52 cards. What is the probability that exactly one of the two cards is an ace?

  1. A.16/221
  2. B.32/221Correct answer
  3. C.8/51
  4. D.4/13

Solution

There are (522)\binom{52}{2} possible two-card selections. To obtain exactly one ace, choose 1 ace from 4 and 1 non-ace from 48, giving 4×484\times48 favourable selections. Hence, the probability is 4×48(522)=1921326=32221\frac{4\times48}{\binom{52}{2}}=\frac{192}{1326}=\frac{32}{221}.

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