To solve this problem, we'll analyze the survey data to calculate the likelihood of each eye color. The survey results are as follows:
- Brown eyes: 35 people
- Blue eyes: 4 people
- Hazel eyes: 10 people
- Green eyes: 1 person
First, we'll determine the total number of people surveyed:
[tex]\[ \text{Total people} = 35 + 4 + 10 + 1 = 50 \][/tex]
Next, we calculate the likelihood (probability) of each eye color by dividing the count of each eye color by the total number of people surveyed.
1. Brown eyes:
[tex]\[ \text{Likelihood of brown eyes} = \frac{35}{50} = 0.7 \][/tex]
2. Blue eyes:
[tex]\[ \text{Likelihood of blue eyes} = \frac{4}{50} = 0.08 \][/tex]
3. Hazel eyes:
[tex]\[ \text{Likelihood of hazel eyes} = \frac{10}{50} = 0.2 \][/tex]
4. Green eyes:
[tex]\[ \text{Likelihood of green eyes} = \frac{1}{50} = 0.02 \][/tex]
Now, let's calculate some percentages for comparison:
- The percentage likelihood of having green eyes:
[tex]\[ 0.02 \times 100 = 2\% \][/tex]
- The percentage likelihood of having brown eyes:
[tex]\[ 0.7 \times 100 = 70\% \][/tex]
Next, let's evaluate each statement:
Statement A:
"The likelihood of having brown eyes is greater than the likelihoods of having blue or green eyes."
[tex]\[
0.7 > 0.08 \quad \text{and} \quad 0.7 > 0.02
\][/tex]
This statement is true.
Statement B:
"The likelihood of having hazel eyes is greater than the likelihood of having blue eyes."
[tex]\[
0.2 > 0.08
\][/tex]
This statement is true.
Statement C:
"The likelihood of having green eyes is 2%."
[tex]\[
0.02 \times 100 = 2\%
\][/tex]
This statement is true.
Statement D:
"The likelihood of having brown eyes is 35%."
[tex]\[
0.7 \times 100 = 70\%
\][/tex]
This statement is false.
Thus, the statement that is not true is:
[tex]\[ \boxed{D} \][/tex]
