Multiple choice

A card is drawn and replaced three times from an ordinary pack of 52 playing cards. The probability that atleast one spade is drawn is

  1. $\displaystyle \frac{9}{64}$
  2. $\displaystyle \frac{1}{64}$
  3. $\displaystyle \frac{37}{64}$
  4. $\displaystyle \frac{3}{64}$
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C Correct answer
Explanation

Probability of drawing a spade is 13/52 = 1/4. Probability of not drawing a spade is 3/4. Probability of no spades in 3 draws = (3/4)^3 = 27/64. Probability of at least one spade = 1 - 27/64 = 37/64.

AI explanation

The probability of drawing a spade is 13/52 or 1/4, so the probability of not drawing a spade is 3/4. The probability of getting no spades in three draws is (3/4)^3, which equals 27/64. Subtracting this from 1 gives the probability of at least one spade, which is 1 - 27/64 = 37/64.

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