Question
A card is drawn one at a time from a well-shuffled deck of 52 cards. In 11 repetitions of this experiment, 2 kings are drawn. If E is the event in which a king is drawn, find the experimental probability \( \mathrm{P}(\mathrm{E}) \). \( \mathrm{P}(\mathrm{E})=\frac{[?]}{[]} \)
Ask by Burgess Ortega. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \mathrm{P}(E) = \frac{2}{11} \)
Solution
1. Identify the number of successes (drawing a king) in the experiment: 2.
2. Identify the total number of experiments (draws): 11.
3. The experimental probability of drawing a king is given by the fraction of successes over the total experiments:
\[
\mathrm{P}(E) = \frac{2}{11}
\]
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Simplify this solution The Deep Dive
The experimental probability is calculated by taking the number of times the event of interest occurs and dividing it by the total number of trials. In this case, you drew 2 kings in 11 repetitions. So, the experimental probability \( \mathrm{P}(E) \) can be calculated as: \[ \mathrm{P}(E) = \frac{\text{Number of kings drawn}}{\text{Total number of draws}} = \frac{2}{11} \] Thus, \( \mathrm{P}(E) = \frac{2}{11} \).
