Question

find the indicated probability. express your answer as a simplified fraction unless otherwise noted.
the table below shows the soft drinks preferences of people in three age groups.
\

$$\begin{tabular}{c|ccc} & cola & root beer & lemon-lime \\\\\\hline under 21 years of age & 40 & 25 & 20 \\\\ between 21 and 40 & 35 & 20 & 30 \\\\ over 40 years of age & 20 & 30 & 35 \\end{tabular}$$

if one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age.
(1 point)
\\(\circ\\) \\(\frac{2}{5}\\)
\\(\circ\\) \\(\frac{3}{5}\\)
\\(\circ\\) \\(\frac{1}{2}\\)
\\(\circ\\) \\(\frac{1}{3}\\)

Explanation:

Step1: Calculate the number of people over 40

Add the values in the "over 40 years of age" row: \(20 + 30+35=85\)

Step2: Use the probability formula

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (people over 40) is \(85\), and the total number of outcomes (total subjects) is \(255\). So \(P = \frac{85}{255}\)

Step3: Simplify the fraction

Divide numerator and denominator by \(85\): \(\frac{85\div85}{255\div85}=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)