14. 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: 4960 of the total applications were for the folk genre. - 192 of the folk applications were for the below 18 category. - 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. [2 marks] b) An application selected at random is found to be under the below 18 categor

Question

14. 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: 

• 960 of the total applications were for the folk genre. 
• 192 of the folk applications were for the below 18 category. 
• 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.               [2 marks]

 b) An application selected at random is found to be under the below 18 category. Find the probability that it is under the folk genre. Show your work.       [2 marks]

Answer 1

total no of applications = 2000

total applications of folk genre = 960

        folk applications for below 18 category = 192

        folk applications for above 18 category = 960 - 192 = 768

total applications of classical genre = 2000 - 960 = 1040

         classical applications for above 18 category = 104

          classical applications for below 18 category = 1040 - 104 = 936

(a) probability that application selected at random is for above 18 category under classical genre:

no of applications above 18 (classical genre) / total no of applications in classical genre

104 / 1040 = 0.1

(b)  probability that application selected at random is for below 18 category under folk genre:

no of applications below 18 (folk genre) / total no of applications in folk genre

192 / 960 = 0.2