Pregunta
A card is drawn one at a time from a well-shuffled deck of 52 cards. In 13 repetitions of this experiment, 2 kings are drawn. If \( E \) is the event in which a king is drawn, find the experimental probability \( P(E) \). \[ P(E)=\frac{[?]}{[]} \]
Ask by Boone Murphy. in the United States
Mar 09,2025
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The experimental probability \( P(E) \) is \( \frac{2}{13} \).
Solución
1. The experimental probability \( P(E) \) is given by the formula:
\[
P(E) = \frac{\text{Number of successes}}{\text{Total number of trials}}
\]
2. In this experiment, a "success" is drawing a king. It is given that 2 kings were drawn in 13 trials.
3. Substituting these values into the formula:
\[
P(E) = \frac{2}{13}
\]
Thus, the experimental probability \( P(E) \) is:
\[
P(E)=\frac{2}{13}
\]
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To find the experimental probability \( P(E) \), you need to divide the number of times the event occurs by the total number of trials. In this case, a king was drawn 2 times in 13 repetitions. Therefore, the experimental probability can be calculated as follows: \[ P(E) = \frac{\text{Number of kings drawn}}{\text{Total number of draws}} = \frac{2}{13} \] So, the answer can be filled in as: \[ P(E)=\frac{2}{13} \]
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