Question

The table shows the results of a survey about eye color.Eye colorNumber of peopleBrown35Blue4Hazel10Green1Use the data in the table to estimate the likelihood that a person has each eyecolor. Which statement is not true?A. The likelihood of having hazel eyes is greater than the likelihood ofhaving blue or green eyes.B. The likelihood of having blue eyes is greater than the likelihood ofhaving green eyes.C. The likelihood of having blue eyes is 4%.D. The likelihood of having brown eyes is 70%.

Answer 1

The likelihood of having blue eyes is 8% and not 4%. Hence, statement C is not true

How to estimate the likelihood (probability) of each eye color

To estimate the likelihood (probability) of each eye color, calculate the proportion of people with each eye color based on the given data.

Total number of people: 35 + 4 + 10 + 1 = 50

A. The likelihood of having hazel eyes is greater than the likelihood of having blue or green eyes:

To calculate the likelihood (probability) of having hazel eyes:

Likelihood of having hazel eyes = Number of people with hazel eyes / Total number of people

= 10 / 50

= 0.2 (or 20%)

To calculate the likelihood (probability) of having blue or green eyes:

Likelihood of having blue or green eyes = (Number of people with blue eyes + Number of people with green eyes) / Total number of people

= (4 + 1) / 50

= 5 / 50

= 0.1 (or 10%)

Therefore, the statement A is true because the likelihood of having hazel eyes (20%) is greater than the likelihood of having blue or green eyes (10%).

B. The likelihood of having blue eyes is greater than the likelihood of having green eyes:

To calculate the likelihood (probability) of having blue eyes:

Likelihood of having blue eyes = Number of people with blue eyes / Total number of people

= 4 / 50

= 0.08 (or 8%)

To calculate the likelihood (probability) of having green eyes:

Likelihood of having green eyes = Number of people with green eyes / Total number of people

= 1 / 50

= 0.02 (or 2%)

Therefore, the statement B is true because the likelihood of having blue eyes (8%) is greater than the likelihood of having green eyes (2%).

C. The likelihood of having blue eyes is 4%:

Based on the previous calculations, the likelihood of having blue eyes is 8% (or 0.08), not 4%. Therefore, statement C is not true.

D. The likelihood of having brown eyes is 70%:

To calculate the likelihood (probability) of having brown eyes:

Likelihood of having brown eyes = Number of people with brown eyes / Total number of people

= 35 / 50

= 0.7 (or 70%)

Therefore, the statement D is true because the likelihood of having brown eyes is indeed 70%.

Answer 2

Given:

The number of people for each eye color

Brown = 35, Blue = 4, Hazel = 10, green = 1

The likelihood of an event e occurring can be calculated using the formula:

`P(an\text{ event e occuring\rparen = }\frac{number\text{ of required outcomes}}{Total\text{ number of possible outcomes}}`

So, we have

Total number of people = 50

Next, we find the likelihood for each event

The likelihood for Brown:

`\begin{gathered} P(brown)\text{ = }(35)/(50) \\ =\text{ }(7)/(10)\text{ } \\ =\text{ 0.7 or 70\%} \end{gathered}`

The likelihood for Blue:

`\begin{gathered} \text{P\lparen blue\rparen = }(4)/(50) \\ =(2)/(25)\text{ or 0.08 or 8\% } \end{gathered}`

The likelihood for Hazel:

`\begin{gathered} P(hazel)\text{ = }(10)/(50) \\ =\text{ }(1)/(5) \end{gathered}`

The likelihood for green:

`P(green)\text{ = }(1)/(50)`

Next, we step through the options and check which is correct

Option A:

The likelihood of blue or green :

`\begin{gathered} =\text{ }(2)/(25)\text{ + }(1)/(50) \\ =\text{ }(4)/(50)\text{ + }(1)/(50) \\ =(5)/(50) \\ =\text{ }(1)/(10) \end{gathered}`

The likelihood of hazel eyes is greater than the likelihood of blue or green

Option B:

The likelihood of having a blue eyes is greater than the likelihood of having green eyes

Incorrect

Option C:

The likelihood of having a blue eyes is 4%

Incorrect

Option D:

The likelihood of having a brown eyes is 70%

This is correct