Question

There are 300 students in an online MBA program for working professionals, for
whom the attendance in online classes is 70%, i.e. on an average, 210 students are
present in an online session. Fifty new students are admitted in this batch.

a. What is the probability of attendance being at least 70% among the new
students, thus ensuring the overall attendance does not fall below 70%?

b. The Program Dean thinks that this probability will increase, if the new batch
size is 40 instead of 50 students. Is he right in assuming so?

Answer 1

Total number of students = 300

Students present in online classes = 70% of 300 = 210

Students admitted = 50




=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=

a.

Total number of students admitted = 50

70% of 50 = 50 × 70 / 100 = 35



So,
Probability = 35 / 50 = 7 / 10



If new batch will be admitted, so new strength will be ( old strength + new strength ) = ( 300 + 50 ) = 350


Total students present including new batch = 210 + 35 = 245



70% of 350 = 350 × 70 / 100

70% of 350 = 245



As 245 = 245, attendance will not fall below 70% , it will be exact 70%




b.

If number of students will be 40 instead of 50,

Total students = 300 + 40 = 340


70% of 40 = 40 × 70 / 100

70% of 40 = 28



Students present = 28



Probability = 28 / 40

Probability = 7 / 10




So, probability will not increase.
$.$

Answer 2

Hi,

Following is the solution to your answer.

Data:

Total number of online students = 300  

Average attendance in online classes = 70% of 300 = 210

New Students admitted = 50  

Solution:  

a. Total number of students admitted = 50  

70% of 50 = 50 × 70 / 100 = 35  

Hence,

Probability = 35 / 50 = 7 / 10

Total number of students after new admissions= old strength + new admissions= total strength

=300+50=350

Average attendance of the new strength= 210+35 or 70% of 350

=245 students

Hence the attendance will remain 70% even after the addition of 50  new students.

b. If number of students will be 40 instead of 50,

Total students = 300 + 40 = 340

70% of 40 = 40 × 70 / 100

70% of 40 = 28

Students present = 28

Probability = 28 / 40

= 7 / 10 i.e. 70% in other words.

Therefor the probability of attendance by decreasing the new admissions will not change.  

Thanks for asking.