Question

Yo! a standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Two cards are randomly drawn without replacement. Calculate the probability of drawing two diamond cards. Express your answer in percent form rounding to the nearest hundredth.

Answer 1

To calculate the probability of drawing two diamond cards, we first need to find the total number of ways to draw 2 cards from a deck of 52 cards. This can be calculated using combinations:

Total number of ways to draw 2 cards = 52 choose 2 = 52! / (2!(52-2)!) = 1326

Next, we need to find the number of ways to draw 2 diamond cards. Since there are 13 diamond cards in the deck, the number of ways to draw 2 diamond cards can be calculated using combinations as well:

Number of ways to draw 2 diamond cards = 13 choose 2 = 13! / (2!(13-2)!) = 78

Finally, we can calculate the probability of drawing two diamond cards by dividing the number of ways to draw 2 diamond cards by the total number of ways to draw 2 cards:

Probability = Number of ways to draw 2 diamond cards / Total number of ways to draw 2 cards = 78 / 1326 ≈ 0.0588

Converting this to a percentage and rounding to the nearest hundredth, the probability of drawing two diamond cards is approximately 5.88%.