A standard deck of 52 cards contains four suits hearts, diamonds clubs in spades each suit has 13 cards ace 234-5678 910 Jack queen 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.
First, we need to find the total number of ways two cards can be drawn from a deck of 52 cards without replacement. This can be calculated using combinations, where we choose 2 cards from 52:
52C2 = 52! / (2!(52-2)!) = 52! / (2!50!) = (52*51) / (2*1) = 1326
Next, we need to find the number of ways to draw two diamond cards. There are 13 diamond cards in the deck, so we can choose 2 from the 13 diamond cards:
13C2 = 13! / (2!(13-2)!) = 13! / (2!11!) = (13*12) / (2*1) = 78
Therefore, the probability of drawing two diamond cards can be calculated by taking the number of ways to draw two diamond cards divided by the total number of ways to draw two cards:
P(drawing two diamond cards) = 78/1326 = 0.0588
To express this probability in percent form, we multiply by 100:
0.0588 * 100 = 5.88%
Therefore, the probability of drawing two diamond cards from a standard deck of 52 cards is 5.88%.