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

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:

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

The likelihood for Blue:

$\begin{gathered} \text{P\lparen blue\rparen = }\frac{4}{50} \\ =\frac{2}{25}\text{ or 0.08 or 8\% } \end{gathered}$

The likelihood for Hazel:

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

The likelihood for green:

$P(green)\text{ = }\frac{1}{50}$

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

Option A:

The likelihood of blue or green :

$\begin{gathered} =\text{ }\frac{2}{25}\text{ + }\frac{1}{50} \\ =\text{ }\frac{4}{50}\text{ + }\frac{1}{50} \\ =\frac{5}{50} \\ =\text{ }\frac{1}{10} \end{gathered}$

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