Certainly! Let's solve this problem step by step.
### Step 1: Determine the Total Number of Repetitions
First, we know that the experiment, which involves drawing a card from a well-shuffled deck of 52 cards, was repeated 11 times. So, the total number of repetitions is:
[tex]$
\text{Total repetitions} = 11
$[/tex]
### Step 2: Identify the Number of Times the Event Occurs
Next, we are given that the event [tex]\(E\)[/tex], which is drawing a king, occurred 2 times in these 11 repetitions. So, the number of times a king was drawn is:
[tex]$
\text{Number of times a king was drawn} = 2
$[/tex]
### Step 3: Calculate the Experimental Probability
The experimental probability [tex]\(P(E)\)[/tex] of an event [tex]\(E\)[/tex] is calculated by dividing the number of times the event occurs by the total number of trials. Therefore, the experimental probability [tex]\(P(E)\)[/tex] is given by:
[tex]$
P(E) = \frac{\text{Number of times a king was drawn}}{\text{Total repetitions}}
$[/tex]
Substituting the given values:
[tex]$
P(E) = \frac{2}{11}
$[/tex]
### Step 4: Simplify the Probability Fraction
In this case, the fraction [tex]\( \frac{2}{11} \)[/tex] is already in its simplest form. Converting this to a decimal for clarification gives approximately:
[tex]$
P(E) \approx 0.18181818181818182
$[/tex]
So, the experimental probability [tex]\(P(E)\)[/tex] of drawing a king in this experiment is:
[tex]$
P(E) = \frac{2}{11} \approx 0.1818
$[/tex]
Therefore, the final result for the experimental probability [tex]\(P(E)\)[/tex] is:
[tex]$
P(E) = \frac{2}{11}
$[/tex]
