Multiple choice

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. The probability of drawing two aces is

  1. $\displaystyle \frac{1}{13}\times \frac{1}{13}$
  2. $\displaystyle \frac{1}{13}\times \frac{1}{17}$
  3. $\displaystyle \frac{1}{52}\times \frac{1}{51}$
  4. $\displaystyle \frac{1}{13}\times \frac{4}{51}$
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A Correct answer
Explanation

Drawing with replacement means the probability of drawing an ace is 4/52 = 1/13 for each draw. The probability of two aces is (1/13) * (1/13).

AI explanation

Because the cards are drawn successively with replacement, the two draws represent independent events using the multiplication rule of probability. The probability of drawing an ace on the first draw is 4 out of 52, which simplifies to 1 over 13. Since the card is replaced, the probability of drawing an ace on the second draw remains 1 over 13, making the combined probability 1 over 13 multiplied by 1 over 13.

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