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 with replacement. Calculate the probability of drawing two diamond cards. Express your answer in percent form rounding to the nearest hundredth.
There are 13 diamond cards in the deck, so the probability of drawing a diamond card on the first draw is $\frac{13}{52}=\frac{1}{4}$. Since the card is replaced before the second draw, the probability of drawing another diamond card is also $\frac{1}{4}$. To find the probability of both events happening (drawing two diamond cards), we multiply the probabilities: $$\frac{1}{4}\times \frac{1}{4}=\frac{1}{16}=0.0625$$ Since the question asks for the probability as a percent rounded to the nearest hundredth, we multiply by 100 and get $\boxed{6.25\%}$.
so what is the answer?
The answer is $\boxed{6.25\%}$.
you sure?
Yes, I am sure. I calculated the probability of drawing two diamond cards to be $\frac{1}{16}$ or $0.0625$, which is equivalent to $6.25\%$ rounded to the nearest hundredth.
are you okay? why are you writing like that..
I apologize if I am causing any confusion. As an AI language model, I am programmed to be objective, concise, and formal in my responses.
so whats the answer?
The answer is $\boxed{6.25\%}$.
To calculate the probability of drawing two diamond cards from a standard deck of 52 cards with replacement, we first need to determine the number of diamond cards in the deck and the total number of possible combinations when drawing two cards.
In a standard deck, there are 13 diamond cards. When drawing the first card, there is a 13/52 (or 1/4) chance of selecting a diamond card since there are 13 diamond cards out of 52 total cards.
Since we are replacing the first card back into the deck before drawing the second card, the probability remains unchanged for the second draw. Therefore, the probability of drawing a second diamond card is also 13/52 (or 1/4).
To find the probability of both events happening, we multiply the probabilities of each event together. So, the probability of drawing two diamond cards is (1/4) * (1/4) = 1/16.
To express this probability in percent form, we multiply by 100 and round to the nearest hundredth. (1/16) * 100 ≈ 6.25%. Therefore, the probability of drawing two diamond cards is approximately 6.25%.