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)
The probability of drawing a diamond on the first draw is 13/52. Since we do not replace the first card, there are now 12 diamond cards left out of 51 cards. Therefore, the probability of drawing another diamond on the second draw is 12/51.
To find the probability of both events happening, we multiply:
(13/52) x (12/51) = 0.0588
This can be expressed as a percentage by multiplying by 100:
0.0588 x 100 = 5.88%
Therefore, the probability of drawing two diamond cards is 5.88%, rounded to the nearest hundredth.
To calculate the probability of drawing two diamond cards from a standard deck of 52 cards, we need to find the number of favorable outcomes (two diamond cards) and divide it by the total number of possible outcomes.
Step 1: Find the number of favorable outcomes:
In a standard deck, there are 13 diamond cards. When we draw the first card, there are 13 diamonds out of 52 total cards. After drawing the first diamond card, there are 12 diamond cards left out of 51 total cards for the second draw.
So, the number of favorable outcomes is calculated as:
13/52 * 12/51 = 156/2652 = 0.0588
Step 2: Find the total number of possible outcomes:
Since we are drawing two cards without replacement, the total number of possible outcomes can be calculated using the combination formula:
C(52, 2) = 52! / (2! * (52-2)!) = 1326
Step 3: Calculate the probability:
Probability = favorable outcomes / total outcomes
Probability = 0.0588 / 1326 = 0.000044
Alternatively, you can multiply the probability by 100 to express it in percent form.
Probability = 0.000044 * 100 = 0.0044%
Therefore, the probability of drawing two diamond cards is approximately 0.0044%.