A standard deck of 52 cards contain four suits heart diamonds cubes and spades. Each suit has 13 cards, ace, 2,3,4,5,6,7,8,9,10, jack, queen, and king. 2 quarts are randomly drawn without replacement, calculate the probability of drawing two diamond cards, express your answer, and form rounding to the nearest hundredth.
There are a total of 52 cards in a standard deck, and 13 of them are diamonds.
To calculate the probability of drawing two diamond cards, we first need to find the total number of ways to draw 2 cards out of 52:
${52 \choose 2} = \frac{52!}{2!(52-2)!} = \frac{52*51}{2} = 1326$
Next, we need to find the number of ways to draw 2 diamond cards out of the 13 diamond cards:
${13 \choose 2} = \frac{13!}{2!(13-2)!} = \frac{13*12}{2} = 78$
Therefore, the probability of drawing two diamond cards is:
$P(\text{two diamond cards}) = \frac{78}{1326} \approx 0.059$
Rounded to the nearest hundredth, the probability of drawing two diamond cards is approximately 0.06.