Question

at a music store in new york city, 70 people entering the store were selected at random and were asked to choose their favorite type of music. of the 70, 20 chose rock, 18 chose country, 4 chose classical and 28 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.)
b) the empirical probability that the next person entering the store favors country music is
(simplify your answer.)
c) the empirical probability that the next person entering the store favors something other than rock, country or classical music is
(simplify your answer.)

Explanation:

Step1: Recall empirical probability formula

Empirical probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Total number of people surveyed \(n = 70\).

Step2: Solve part (a)

Number of people who chose rock \(=30\). So, \(P(\text{rock})=\frac{30}{70}=\frac{3}{7}\).

Step3: Solve part (b)

Number of people who chose country \(=18\). So, \(P(\text{country})=\frac{18}{70}=\frac{9}{35}\).

Step4: Solve part (c)

Number of people who chose something other than rock, country or classical \(=20\). So, \(P(\text{other})=\frac{20}{70}=\frac{2}{7}\).

Answer:

a) \(\frac{3}{7}\)
b) \(\frac{9}{35}\)
c) \(\frac{2}{7}\)