A standard deck of cards 52 contains 4 suits, heart diamond clubs and spade.Each suit has 13 cards 8 2 3 4 5 6 7 8 9 10 Jack Queen king.2 guards are randomly drawn without replacement.Calculate the probability of drawing two diamond cards
There are 13 diamond cards in the deck.
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 cards:
${52 \choose 2} = \frac{52!}{2!(52-2)!} = 1326$
Next, we calculate the number of ways to draw 2 diamond cards out of 13 diamond cards:
${13 \choose 2} = \frac{13!}{2!(13-2)!} = 78$
Therefore, the probability of drawing two diamond cards can be calculated as:
$P(\text{2 diamond cards}) = \frac{\text{Number of ways to draw 2 diamond cards}}{\text{Total number of ways to draw 2 cards}} = \frac{78}{1326} = \frac{26}{442} \approx 0.0588$
So, the probability of drawing two diamond cards is approximately 0.0588 or 5.88%.