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) show why that is the answer
First, we need to find the total number of ways to draw 2 cards out of 52 without replacement. This can be calculated using the combination formula:
52 choose 2 = (52!)/(2!(52-2)!) = (52*51)/(2*1) = 1326
Next, we need to find the number of ways to draw 2 diamond cards out of 13 diamond cards. This can be calculated using the combination formula as well:
13 choose 2 = (13!)/(2!(13-2)!) = (13*12)/(2*1) = 78
So, the probability of drawing two diamond cards is:
78/1326 = 0.05882352941
Converting this to percent form and rounding to the nearest hundredth:
0.05882352941 * 100 ≈ 5.88%
Therefore, the probability of drawing two diamond cards from a standard deck of 52 cards is approximately 5.88%.
do it simpler
Sure! Another way to solve this problem is to find the probability of drawing the first diamond card and the second diamond card separately and then multiply the probabilities.
The probability of drawing the first diamond card is 13/52 since there are 13 diamond cards out of 52 total cards.
After drawing the first diamond card, there are now 12 diamond cards left out of 51 total cards, so the probability of drawing the second diamond card is 12/51.
To find the overall probability, we multiply the probabilities of drawing two diamond cards in sequence:
(13/52) * (12/51) = 0.05882352941
Converting this to percent form and rounding to the nearest hundredth:
0.05882352941 * 100 ≈ 5.88%
Therefore, the probability of drawing two diamond cards from a standard deck of 52 cards is approximately 5.88%.