Question

the people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. the results of the survey are shown in the table.

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$$\begin{tabular}{|c|c|} \\hline eye color & number of people \\\\ \\hline brown & 20 \\\\ \\hline green & 6 \\\\ \\hline blue & 17 \\\\ \\hline hazel & 7 \\\\ \\hline \\end{tabular}$$

what is the probability that a person chosen at random from this group has brown or green eyes?

\\(\bigcirc \frac{3}{25}\\)
\\(\bigcirc \frac{7}{25}\\)
\\(\bigcirc \frac{13}{25}\\)
\\(\bigcirc \frac{17}{25}\\)

Explanation:

Calculate the total number of people surveyed

Using the Theoretical Probability knowledge point

$$ \text{Total} = 20 + 6 + 17 + 7 = 50 $$

Find the number of favorable outcomes

Using the Mutually Exclusive Events and Probability Addition Rule knowledge points

$$ \text{Favorable} = \text{brown} + \text{green} = 20 + 6 = 26 $$

Compute the probability

Using the Theoretical Probability knowledge point

$$ P(\text{brown or green}) = \frac{26}{50} = \frac{13}{25} $$

Answer:

• (A) \(\frac{3}{25}\)
• (B) \(\frac{7}{25}\)
• (C) \(\frac{13}{25}\) (Correct answer)
• (D) \(\frac{17}{25}\)