Multiple choice

5 cards are drawn successively from a well-shuffled pack of 52 cards with replacement. Determine the probability that all the five cards should be spades?

  1. $1/1225$
  2. $1/1125$
  3. $1/125$
  4. $1/1025$
  5. $1/1050$
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D Correct answer
Explanation

Drawing 5 cards with replacement means each draw is independent. The probability of drawing a spade in one draw is 13/52 = 1/4. For 5 successive draws with replacement, the probability is (1/4)^5 = 1/1024. Therefore, 1/1025 is the closest option. The calculation assumes a standard deck with 13 spades out of 52 cards.

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