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)
There are a total of 52 cards in a standard deck, and there are 13 diamond cards out of the 52.
When drawing the first diamond card, the probability is 13/52 = 1/4.
After drawing the first diamond card, there are now 51 cards remaining, and only 12 of them are diamonds.
So the probability of drawing a second diamond card is 12/51 = 4/17.
To find the probability of drawing two diamond cards, we multiply the probabilities of drawing the first and second diamond cards together: (1/4) * (4/17) = 1/17.
To express this probability in percentage form, we convert it to a decimal: 1/17 ≈ 0.0588.
And then we convert the decimal to a percentage: 0.0588 * 100 ≈ 5.88%.
Therefore, the probability of drawing two diamond cards is approximately 5.88%.
I didn't ask for the approximate answer.
I apologize for that. Let's find the exact probability of drawing two diamond cards:
The probability of drawing the first diamond card is 13/52 = 1/4.
After drawing the first diamond card, there are 12 diamond cards left out of the remaining 51 cards.
So, the probability of drawing the second diamond card, given that the first card drawn was a diamond, is 12/51 = 4/17.
To find the probability of drawing two diamond cards, we multiply the probabilities of drawing the first and second diamond cards:
(1/4) * (4/17) = 4/68 = 1/17.
Therefore, the exact probability of drawing two diamond cards is 1/17, which is approximately 0.0588 or 5.88% when expressed in percentage form.
So, the probability of drawing two diamond cards is 1/17, or approximately 5.88%.
Use the table to answer the question.
Compound Event | Total Number of Occurrences
Heads and Yellow | 9
Heads and Red | 3
Heads and Blue | 4
Heads and Green | 1
Tails and Yellow | 6
Tails and Red | 7
Tails and Blue | 2
Tails and Green | 3
A student had a spinner and a coin. The student was running an experiment for math class. The spinner had an equal chance of landing on 4 colors: yellow, red, blue, and green. The student flipped the coin and spun the spinner, and the results are recorded in the table.
If the student were to flip the coin and spin the spinner 130 times, how many times would the result be tails and red?
(1 point)
From the table, we see that the occurrence of Tails and Red is 7.
So, if the student were to flip the coin and spin the spinner 130 times, the number of times the result would be Tails and Red would be:
7/130 * 130 = 7.
Therefore, the result of Tails and Red would occur 7 times out of 130 trials.
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.
(4 points)
The total number of marbles in the bowl is 120.
Out of the 120 marbles, 80 are black, 28 are white, and the rest are red. To find the number of red marbles, we subtract the number of black and white marbles from the total:
Number of red marbles = Total marbles - Black marbles - White marbles
Number of red marbles = 120 - 80 - 28
Number of red marbles = 12
So, there are 12 red marbles in the bowl.
The probability of Nicole pulling a red marble out of the bowl is given by:
Probability = Number of red marbles / Total number of marbles
Probability = 12 / 120
Probability = 1 / 10
Therefore, the probability that Nicole will pull a red marble out of the bowl is 1/10 or 0.1.