Multiple choice

5 cards are drawn one after an other successively with replacement from a well shuffled pack of 52 cards. The probability that none is a spade is

  1. 1-$(\displaystyle \frac{3}{4})^{5}$
  2. $(\displaystyle \frac{3}{4})^{5}$
  3. $(\displaystyle \frac{1}{4})^{5}$
  4. 1-$(\displaystyle \frac{1}{4})^{5}$
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B Correct answer
Explanation

The probability of drawing a spade is 13/52 = 1/4. The probability of NOT drawing a spade is 3/4. Since the cards are drawn with replacement, the probability that none of the 5 cards is a spade is (3/4)^5.

AI explanation

A pack of 52 cards contains 13 spades, so the probability of drawing a spade is 13 divided by 52, which is 1/4. The probability of not drawing a spade in a single draw is 1 minus 1/4, which is 3/4. Because the 5 cards are drawn successively with replacement, the events are independent, meaning we raise the single event probability to the power of 5. The probability that none is a spade is (3/4)^5.

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