Multiple choice

$4$ cards are drawn from the deck of $52$ cards. Find the probability of all $4$ cards drawn being Diamond if the cards are replaced.

  1. $\dfrac {1}{256}$
  2. $\dfrac {22}{4156}$
  3. $\dfrac {25}{4156}$
  4. $\dfrac {60}{4156}$
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A Correct answer
Explanation

Probability of drawing a diamond = 13/52 = 1/4. Since cards are replaced, each draw is independent. Probability of 4 diamonds = (1/4)^4 = 1/256.

AI explanation

Because the cards are replaced, the binomial distribution formula is used with the probability of drawing a diamond being 13/52, or 1/4. The probability of drawing four diamonds in four independent trials is (1/4)^4. This calculation results in 1/256.

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