Eric is randomly drawing cards from a deck of 52. He first draws a red card, places it back in the deck, shuffles the deck, and then draws another card.What is the probability of drawing a red card, placing it back in the deck, and drawing another red card? Answer choices are in the form of a percentage, rounded to the nearest whole number.4%13%22%25%
Question
Eric is randomly drawing cards from a deck of 52. He first draws a red card, places it back in the deck, shuffles the deck, and then draws another card.What is the probability of drawing a red card, placing it back in the deck, and drawing another red card? Answer choices are in the form of a percentage, rounded to the nearest whole number.4%13%22%25%
Solution
The deck of 52 cards consists of 26 red cards (13 hearts and 13 diamonds).
Step 1: Calculate the probability of drawing a red card on the first draw. This is 26 (the number of red cards) out of 52 (the total number of cards), which simplifies to 1/2 or 50%.
Step 2: Because Eric places the card back in the deck and shuffles it, the probability of drawing a red card on the second draw remains the same, 1/2 or 50%.
Step 3: To find the probability of both events happening (drawing a red card, replacing it, and drawing another red card), you multiply the probabilities of the individual events.
So, 50% (probability of first red card) * 50% (probability of second red card) = 25%.
Therefore, the answer is 25%.
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