Question
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)
To calculate the probability of drawing two diamond cards, we first need to determine the total number of ways to draw 2 cards from a standard deck of 52 cards, and then determine the number of ways to draw 2 diamond cards.
Total ways to draw 2 cards from 52 cards:
There are ${52 \choose 2}$ ways to draw 2 cards from a deck of 52. This is equal to 1326.
Number of ways to draw 2 diamond cards:
There are 13 diamond cards in the deck, so we can choose 2 diamond cards in ${13 \choose 2}$ ways. This is equal to 78.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 78 / 1326
Probability ≈ 0.0588
Convert to percent form:
0.0588 * 100 = 5.88%
Therefore, the probability of drawing two diamond cards is approximately 5.88%.