A survey was conducted among 500 students about their preferred extracurricular activity
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A survey was conducted among 500 students about their preferred extracurricular activity. The results are shown below:
• Music Club: 135 students
• Art Club: 110 students
• Science Club: 95 students
• Sports Club: 140 students
• Drama Club: 20 students
Use the survey data to answer the following questions. Show all working.
(i) Calculate the empirical probability for a randomly chosen student to prefer each club. Present each probability as (a) a fraction in simplest form and (b) a decimal correct to three decimal places.
(ii) List the clubs in order from most preferred to least preferred on the basis of their empirical probabilities.
(iii) Identify any pair of clubs that are equally likely to be preferred. If no such pair exists, state that explicitly and justify your answer.
(iv) The school wants to claim that joining the Drama Club is an "impossible choice" for students. Using the range property of probability and the value you obtained in part (i), comment on the validity of this claim.
(v) Suppose 250 more students are surveyed and the proportions for each club remain unchanged. Predict how many of these additional students would be expected to choose the Science Club. Give your answer to the nearest whole number and explain your calculation.