Multiple choice

Four cards are drawn successively from a pack of 52 cards. What is the probability of drawing all cards of different suits, if cards are replaced?

  1. 1/32

  2. 1/16

  3. 3/32

  4. 3/16

  5. 5/48
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C Correct answer
Explanation

Probability of picking a specific suit is 1/4. Since cards are replaced, each draw is independent. Probability of picking 4 different suits in 4 draws is 4! * (1/4)^4 = 24 / 256 = 3/32.

AI explanation

With replacement, the draws are independent events, and the probability of drawing any specific suit remains 13 out of 52, or 1/4, on each draw. To get one card from each of the four suits, the probability is the number of ways to arrange the four suits multiplied by the probability of drawing each suit. The number of permutations of the four suits is 4 factorial, which is 24, so the probability is 24 times (1/4) multiplied by itself 4 times, yielding 24 divided by 256, which simplifies to 3/32.

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