Question

at a music store in new york city, 72 people entering the store were selected at random and were asked to choose their favorite type of music. of the 72, 20 chose rock, 18 chose country, 6 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.)

Explanation:

Identify the given values

We have a total sample size of \(72\) people.
The frequencies for each music category are:

• Rock: \(20\)
• Country: \(18\)
• Classical: \(6\)
• Other: \(28\)

Calculate empirical probability for rock

The empirical probability is the ratio of the frequency of the event to the total number of trials.
Using the Empirical Probability concept:

$$ P(\text{Rock}) = \frac{20}{72} $$

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, \(4\):

$$ P(\text{Rock}) = \frac{5}{18} $$

Calculate empirical probability for country

Using the Empirical Probability concept:

$$ P(\text{Country}) = \frac{18}{72} $$

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, \(18\):

$$ P(\text{Country}) = \frac{1}{4} $$

Calculate empirical probability for other

Using the Empirical Probability concept:

$$ P(\text{Other}) = \frac{28}{72} $$

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, \(4\):

$$ P(\text{Other}) = \frac{7}{18} $$

Answer:

Question a

The empirical probability that the next person entering the store favors rock music is <blank>\(\frac{5}{18}\)</blank>.

Question b

The empirical probability that the next person entering the store favors country music is <blank>\(\frac{1}{4}\)</blank>.

Question c

The empirical probability that the next person entering the store favors something other than rock, country, or classical music is <blank>\(\frac{7}{18}\)</blank>.