Question

at a music store in new york city, 54 people entering the store were selected at random and were asked to choose their favorite type of music. of the 54, 20 chose rock, 12 chose country, 2 chose classical and 20 chose something other than rock, country, or classical.
a) determine the empirical probability that the next person entering the store favors rock music.
b) determine the empirical probability that the next person entering the store favors country music.
c) determine the empirical probability that the next person entering the store favors something other than rock, country, or classical music.
a) the empirical probability that the next person entering the store favors rock music is \\(\frac{10}{27}\\)
(simplify your answer)
b) the empirical probability that the next person entering the store favors country music is \\(\square\\)
(simplify your answer)

Explanation:

Step1: Recall the formula for empirical probability

Empirical probability \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of people surveyed \(n = 54\).

Step2: Calculate the empirical probability for country music

For country music, the number of favorable outcomes (people who chose country) \(m=12\). Using the formula \(P=\frac{m}{n}\), we substitute \(m = 12\) and \(n = 54\). So \(P=\frac{12}{54}\).

Step3: Simplify the fraction

We can simplify \(\frac{12}{54}\) by dividing both the numerator and the denominator by their greatest - common divisor. The GCD of 12 and 54 is 6. \(\frac{12\div6}{54\div6}=\frac{2}{9}\)

Answer:

The empirical probability that the next person entering the store favors country music is \(\frac{2}{9}\)