CMI-2021-DataScience-B: 4

Question

The $\text{CMI MSc DS 2021}$ batch of $60$ students is holding an online event to celebrate their joining $\text{CMI.}$ Student Aruni is in charge of organizing the musical section, and she sends out an online form where each student has to mark whether they agree or decline to performing two activities during the event: singing, and playing a musical instrument. Each student can mark one of four sets of choices: 

1. agree to both singing and playing an instrument,
2. agree to sing and decline to play an instrument,
3. agree to play an instrument and decline to sing, or
4. decline to do either activity.

All the students respond within the deadline, and Aruni sits down to tabulate the results so that she can plan the musical events. She finds that thirty five students agreed to sing or play an instrument, of whom twenty students agreed to do both.

How many students agreed to do exactly one activity, and how many declined to participate?

Answer 1

The ven diagram of the problem :-

It is given ,

$|S\cup I|=35$

$|S\cap_{}^{} I|=20$

So number of Student who are doing exactly one activity is the red and violet portion , which we can easily found by ,

$|S\cup I|$ – $|S\cap_{}^{} I|$ $=35-20=15$

So, $15$ student agreed to do exactly one activity.

No of Student decline to participate is = total number of student – no of student agreed to participate at least one of the activity

                                                            $=60  – $$|S\cup I|$

                                                             $=25$

 So ,$25$ student decline to do any activity.