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
(simplify your answer.)

Explanation:

Step1: Recall the formula for empirical probability

Empirical probability \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)

Step2: Identify the values for part (a)

For rock music, the number of favorable outcomes (people who chose rock) is \(n = 20\), and the total number of outcomes is \(N=54\)
So, \(P(\text{rock})=\frac{20}{54}\)

Step3: Simplify the fraction

Divide numerator and denominator by 2: \(\frac{20\div2}{54\div2}=\frac{10}{27}\)

Answer:

\(\frac{10}{27}\)