Multiple choice

Two cards are drawn at random form a pack of $52$ cards. The probability that both are the cards of spade is

  1. $\dfrac{1}{26}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{1}{17}$
  4. $\dfrac{1}{52}$
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C Correct answer
Explanation

The probability of drawing one spade is 13/52 = 1/4. Since two cards are drawn, the probability of both being spades is (13/52) * (12/51) = (1/4) * (4/17) = 1/17.

AI explanation

Using the combination formula for drawing cards without replacement, the required probability is the ratio of choosing 2 spades from the 13 available to choosing 2 cards from the 52 in the deck. This sets up as 13C2 divided by 52C2, which equals 78 divided by 1326. Simplifying this fraction gives the result 1 divided by 17, making the probability 1/17.

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