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.(1 point
First, we need to find the total number of ways to draw 2 cards from a deck of 52 cards, without replacement. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of cards in the deck (52) and r is the number of cards being drawn (2):
C(52, 2) = 52! / (2!(52-2)!) = (52*51) / (2*1) = 1326
Next, we need to find the number of ways to draw 2 diamond cards. There are 13 diamond cards in a deck, so the number of ways to draw 2 diamond cards can be calculated as:
C(13, 2) = 13! / (2!(13-2)!) = (13*12) / (2*1) = 78
Finally, we 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 = 78 / 1326 ≈ 0.0588
Converting this to a percentage rounded to two decimal places, we get:
Probability in percent form ≈ 5.88%