To find the experimental probability [tex]\( P(E) \)[/tex] of drawing a king from a well-shuffled deck of 52 cards, based on the given information, let's break down the steps clearly.
1. Determine the number of experiments:
We are told that the card drawing experiment was repeated 11 times. Therefore, the total number of experiments [tex]\( n \)[/tex] is 11.
[tex]\[ \text{Number of experiments} = n = 11 \][/tex]
2. Determine the number of successful outcomes:
Success, in this case, is defined as drawing a king. It is given that, out of the 11 draws, a king was drawn 2 times. Therefore, the number of successful outcomes [tex]\( k \)[/tex] is 2.
[tex]\[ \text{Number of times a king is drawn} = k = 2 \][/tex]
3. Calculate the experimental probability:
The experimental probability, [tex]\( P(E) \)[/tex], is given by the ratio of the number of successful outcomes to the total number of experiments. This can be represented as:
[tex]\[ P(E) = \frac{k}{n} \][/tex]
Substituting the values we have determined:
[tex]\[ P(E) = \frac{2}{11} \][/tex]
4. Convert fraction to decimal (optional but helpful for interpretation):
[tex]\[ P(E) = \frac{2}{11} \approx 0.1818 \][/tex]
Therefore, the experimental probability [tex]\( P(E) \)[/tex] of drawing a king is:
[tex]\[ P(E) = \frac{2}{11} \][/tex]
In decimal form, this is approximately 0.1818, or 18.18% when expressed as a percentage. Thus, based on the experimental results, the likelihood of drawing a king in a single draw from this well-shuffled deck of cards is [tex]\( \frac{2}{11} \)[/tex].
