Question
A card is drawn one at a time from a well-shuffled deck of 52 cards. In 11 repetitions of this experiment, 1 king is drawn. If \( E \) is the event in which a king is drawn, find the experimental probability \( P(E) \). \[ P(E)=\frac{[?]}{[]} \]
Ask by Savage Rodriquez. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The experimental probability \( P(E) \) is \( \frac{1}{11} \).
Solution
Given that a king was drawn once in 11 trials, the number of times the event \(E\) (drawing a king) occurred is 1, and the total number of experiments is 11.
The experimental probability is given by
\[
P(E)=\frac{\text{number of kings drawn}}{\text{total trials}}=\frac{1}{11}.
\]
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Simplify this solution Beyond the Answer
To find the experimental probability \( P(E) \), we use the formula: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}. \] In this case, you drew a king once in 11 trials. Therefore, the number of favorable outcomes (drawing a king) is 1, and the total number of trials is 11. Substituting these values into the formula gives us: \[ P(E) = \frac{1}{11}. \] So, the experimental probability \( P(E) = \frac{1}{11} \).
