Multiple choice

5 cards are drawn one after an other successively with replacement from a well shuffled pack of 52 cards. The probability that all the 5 cards are spades

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

Probability of drawing a spade in one draw is 13/52 = 1/4. Since draws are with replacement, the probability of drawing 5 spades in a row is (1/4) * (1/4) * (1/4) * (1/4) * (1/4) = (1/4)^5.

AI explanation

The probability of drawing a spade from a standard deck is 13/52, which simplifies to 1/4. Because the draws are independent and completed with replacement, multiply the probability of drawing a spade five times. This results in (1/4)^5.

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