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.

	cola	root beer	lemon-lime
between 21 and 40	35	20	30
over 40 years of age	20	30	35

if one of the 255 subjects is randomly selected, find the probability that the person is over 40 and prefers cola.
(1 point)
\\(\bigcirc\\) \\(\frac{4}{19}\\)
\\(\bigcirc\\) \\(\frac{4}{17}\\)
\\(\bigcirc\\) \\(\frac{4}{51}\\)
\\(\bigcirc\\) \\(\frac{32}{51}\\)

Explanation:

Step1: Find the number of favorable outcomes

From the table, the number of people over 40 years of age who prefer cola is 20.

Step2: Find the total number of outcomes

The total number of subjects is 255.

Step3: Calculate the probability

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So, \(P = \frac{20}{255}\). Simplify the fraction: \(\frac{20\div5}{255\div5}=\frac{4}{51}\)

Answer:

\(\frac{4}{51}\) (the third option)