Multiple choice

If two cards are selected at random from a standard deck of $52$ cards, what is the probability that they will both be diamonds?

  1. $\dfrac {1}{13}$
  2. $\dfrac {1}{4}$
  3. $\cfrac{1}{17}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ways to pick 2 cards = 52C2 = (52*51)/2 = 1326. Ways to pick 2 diamonds = 13C2 = (13*12)/2 = 78. Probability = 78/1326 = 1/17.

AI explanation

The total number of ways to select 2 cards from a standard deck of 52 cards is calculated using the combination formula 52C2, which equals 1326. Since there are 13 diamonds in the deck, the number of ways to select 2 diamonds is 13C2, which equals 78. Using the classical probability formula, the required probability is 78 divided by 1326, which simplifies to 1/17. Therefore, the probability that both cards are diamonds is 1/17, making the result 1/17.

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