Question
A randomly selected card from a standard 52 -card deck is noted. The card is then replaced. Do it repeated for a total of 3 times. The answer should be a fraction. The chance that 3 Queens are randomly selected (with replacement) is:- Enter your answer
Ask by Hodgson Washington. in the United States
Feb 04,2025
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Tutor-Verified Answer
Answer
The probability of drawing 3 Queens in a row with replacement is \(\frac{1}{2197}\).
Solution
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Bonus Knowledge
The probability of drawing a Queen from a standard 52-card deck is 4 out of 52, as there are 4 Queens in the deck. This simplifies to \( \frac{1}{13} \). Since the draws are independent and with replacement, you multiply the probabilities for each draw. Thus, the probability of drawing 3 Queens is: \[ \left(\frac{1}{13}\right) \times \left(\frac{1}{13}\right) \times \left(\frac{1}{13}\right) = \frac{1}{13^3} = \frac{1}{2197} \] So, the answer is: \( \frac{1}{2197} \).