Multiple choice

Three cards are drawn from a pack of $52$ cards with replacement. Find the probability of getting three ace cards.

  1. $\dfrac{1}{7898}$
  2. $\dfrac{1}{2244}$
  3. $\dfrac{1}{2197}$
  4. $\dfrac{5}{8098}$
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C Correct answer
Explanation

Probability of drawing an ace is 4/52 = 1/13. Since it is with replacement, the probability of drawing three aces is (1/13)^3 = 1/2197.

AI explanation

Using the binomial distribution for independent events, the probability of drawing three aces with replacement is the product of the individual probabilities. The probability of drawing an ace in a single draw from a 52-card deck is 4 divided by 52, which simplifies to 1 divided by 13. Because the cards are replaced, the probability of getting three aces in three draws is 1/13 multiplied by itself three times, resulting in 1/2197.

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