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

Answer 1

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%.