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.
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There are 13 diamond cards out of a total of 52 cards. Thus, the probability of drawing a diamond card on the first draw is 13/52. After one diamond card is drawn, there are 12 diamond cards left in a remaining deck of 51 cards. Thus, the probability of drawing a second diamond card is 12/51. To find the probability of both events occurring together, we multiply the probabilities:
(13/52) * (12/51) = 0.0588
To convert to percent form, we multiply by 100:
0.0588 * 100 = 5.88%
Rounding to the nearest hundredth, the probability of drawing two diamond cards is 5.88%.
Nicole pulls a colored marble out of a bowl, choosing the marble at random. There are 120 marbles in the bowl, of which 80 are black, 28 are white, and the rest are red. Use words and numbers to describe the probability that she will pull a red marble out of the bowl. Show your work.
The total number of marbles in the bowl is 120. Of these, 80 are black, 28 are white, and the rest are red. We can find the number of red marbles by subtracting the number of black and white marbles from the total:
Number of red marbles = Total number of marbles - Number of black marbles - Number of white marbles
Number of red marbles = 120 - 80 - 28 = 12
Therefore, there are 12 red marbles in the bowl.
The probability of pulling a red marble out of the bowl can be expressed as:
Probability of red marble = Number of red marbles / Total number of marbles
Probability of red marble = 12 / 120
Probability of red marble = 0.1
We can also express this probability as a percentage by multiplying by 100:
Probability of red marble = 0.1 * 100%
Probability of red marble = 10%
Therefore, there is a 10% chance that Nicole will pull a red marble out of the bowl.
To calculate the probability of drawing two diamond cards from a standard deck of 52 cards, we need to determine the number of favorable outcomes (the number of ways to draw two diamond cards) and the total number of possible outcomes (all possible ways to draw two cards).
Step 1: Determine the number of favorable outcomes.
The number of diamond cards in a standard deck is 13. Now, since two cards are drawn without replacement, we need to calculate the number of ways to choose 2 diamond cards out of the 13. This can be calculated using the combination formula: C(n, r) = n! / (r! * (n - r)!)
In this case, n = 13 (the number of diamond cards) and r = 2 (the number of cards drawn).
Using the combination formula: C(13, 2) = 13! / (2! * (13 - 2)!) = 13! / (2! * 11!) = (13 * 12) / (2 * 1) = 78
Step 2: Determine the total number of possible outcomes.
The total number of ways to draw two cards from a standard deck of 52 cards can be calculated using the combination formula again, but this time n = 52 (the number of cards in the deck) and r = 2 (the number of cards drawn).
Using the combination formula: C(52, 2) = 52! / (2! * (52 - 2)!) = 52! / (2! * 50!) = (52 * 51) / (2 * 1) = 1326
Step 3: Calculate the probability.
The probability of drawing two diamond cards is equal to the number of favorable outcomes divided by the total number of possible outcomes.
Probability = favorable outcomes / total outcomes = 78 / 1326
Probabiity = 0.0587
Converting this probability to percent form, rounding to the nearest hundredth, we get 5.87%.
To calculate the probability of drawing two diamond cards, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When two cards are drawn without replacement from a standard deck of 52 cards, the total number of possible outcomes can be calculated using the "choose" formula. Since we are selecting 2 cards out of 52 without replacement, the total number of possible outcomes is given by:
52 choose 2 = (52! / (2!(52-2)!))
Number of favorable outcomes:
Since we are interested in drawing two diamond cards, there are 13 diamond cards in total. When we draw two of them, the number of favorable outcomes is given by:
13 choose 2 = (13! / (2!(13-2)!))
Now, let's calculate the probability using the formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = [(13 choose 2) / (52 choose 2)] * 100%
Calculating these values, we have:
Probability = [(13! / (2!(13-2)!)) / (52! / (2!(52-2)!))] * 100%
Simplifying this expression:
Probability = [(13! * (52-2)! * 2!) / (2! * (13-2)! * 52!)] * 100%
Probability = (13 * 12 / 52 * 51) * 100%
Probability = 0.0588 * 100%
Probability = 5.88%
Therefore, the probability of drawing two diamond cards is 5.88%.