Multiple choice

If $2$ cards are drawn from a well shuffled pack of $52$ cards, the probability that they are of the same colours without replacement is:

  1. $\dfrac{1}{2}$
  2. $\dfrac{26}{51}$
  3. $\dfrac{25}{51}$
  4. $\dfrac{25}{102}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ways to draw 2 cards = C(52,2) = 1326. Ways to draw 2 of same color = C(26,2) + C(26,2) = 325 + 325 = 650. Probability = 650/1326 = 25/51.

AI explanation

The total ways to draw two cards is 52C2, which is 1326. The number of ways to draw two red cards is 26C2, which is 325, and there are also 325 ways to draw two black cards. Using the classical probability formula, adding the same color possibilities gives 650/1326, which simplifies to 25/51. The result is 25/51.

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