Question

Read the information given below and answer the questions that follow.

For an audition of a reality singing competition, interested candidates were asked to apply under one of the two musical genres - folk or classical and under one of the two age categories - below 18 or 18 and above.

The following information is known about the 2000 applications received:
a. 960 of the total applications were for the folk genre.
b. 192 of the folk applications were for the below 18 category.
c. 104 of the classical applications were for the 18 and above category.

a) What is the probability that an application selected at random is for the 18 and above category provided it is under the classical genre? Show your work.

Answer 1

The probability that a randomly selected application is for the 18 and above category within the classical genre is 0.10 or 10%.

Step-by-step explanation:

The probability that an application selected at random is for the 18 and above category provided it is under the classical genre can be found by considering the given information. Since we are told that 960 of the 2000 applications are for the folk genre, the remaining 1040 applications must be for the classical genre because the total number of applications is 2000 (2000 - 960 = 1040). Furthermore, we know that 104 of the classical applications are for the 18 and above category.

To find the probability, we use the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

Here, the number of favorable outcomes is the number of classical applications for the 18 and above category, which is 104. The total number of possible outcomes is the total number of classical applications, which is 1040. Therefore, the probability is:

Probability = 104 / 1040 = 0.10 or 10%.