To solve this problem, we need to determine the probability that an archer hits zero bull's eyes. The probability can be found by dividing the number of archers who hit zero bull's eyes by the total number of archers.
Let's break down the given information step-by-step:
1. Total number of archers: 50
2. Frequencies of bull's eyes hits:
- 0 bull's eyes: 3 archers
- 1 bull's eyes: 5 archers
- 2 bull's eyes: 7 archers
- 3 bull's eyes: 7 archers
- 4 bull's eyes: 11 archers
- 5 bull's eyes: 10 archers
- 6 bull's eyes: 7 archers
3. Calculate the probabilities for each frequency:
- The probability of hitting 0 bull's eyes is the number of archers hitting 0 bull's eyes divided by the total number of archers.
[tex]\[
\text{Probability of hitting 0 bull's eyes} = \frac{3}{50}
\][/tex]
4. Let’s verify the other probabilities as given:
- Probability of hitting 1 bull's eye: [tex]\(\frac{5}{50} = 0.1\)[/tex]
- Probability of hitting 2 bull's eyes: [tex]\(\frac{7}{50} = 0.14\)[/tex]
- Probability of hitting 3 bull's eyes: [tex]\(\frac{7}{50} = 0.14\)[/tex]
- Probability of hitting 4 bull's eyes: [tex]\(\frac{11}{50} = 0.22\)[/tex]
- Probability of hitting 5 bull's eyes: [tex]\(\frac{10}{50} = 0.2\)[/tex]
- Probability of hitting 6 bull's eyes: [tex]\(\frac{7}{50} = 0.14\)[/tex]
Given the above calculations, the missing probability for the event where an archer hits zero bull's eyes is:
[tex]\[
\frac{3}{50} = 0.06
\][/tex]
Now, let's match the answer to the given multiple choice options:
- A. [tex]\(\frac{3}{50}\)[/tex]
- B. [tex]\(\frac{17}{50}\)[/tex]
- C. [tex]\(\frac{4}{50}\)[/tex]
- D. [tex]\(\frac{3}{5}\)[/tex]
The correct answer is A. [tex]\(\frac{3}{50}\)[/tex].
