To find the experimental probability [tex]\( P(E) \)[/tex] of drawing a king from a well-shuffled deck of 52 cards, given that in 11 repetitions of this experiment, 2 kings were drawn, let's go through the steps:
1. Identify the total number of repetitions of the experiment:
In this case, the card was drawn 11 times. Therefore, the total number of repetitions is 11.
2. Determine the number of successful events:
A successful event is defined as drawing a king. According to the question, 2 kings were drawn in these 11 repetitions. So, the number of successful events is 2.
3. Calculate the experimental probability:
The experimental probability [tex]\( P(E) \)[/tex] is the ratio of the number of successful events to the total number of repetitions. It is given by:
[tex]\[
P(E) = \frac{\text{Number of successful events}}{\text{Total number of repetitions}}
\][/tex]
4. Substitute the values into the formula:
[tex]\[
P(E) = \frac{2}{11}
\][/tex]
5. Convert the fraction to a decimal (if desired, but not necessary for this format):
[tex]\[
P(E) = \frac{2}{11} \approx 0.1818 \ldots
\][/tex]
Therefore, the experimental probability [tex]\( P(E) \)[/tex] that a king is drawn is:
[tex]\[
P(E) = \frac{2}{11}
\][/tex]
