Predicting Absenteeism: Comparing Binomial Distribution in Two Classes

[aaaa202]

Homework Statement

In a class with 20 and one with 10 students each student has a probability of 0.3 to not show up on a particular day. On a given day, which class is most likely to have the highest ratio of absent students? This was in my exam, unfortunately I did not know how to do it.

Homework Equations

The probability that n students are absent on a given day in one class is binomially distributed.
I heard some say that since the relative standard deviation goes like 1/√N the class with fewer pupils is most likely to have most absent, but I am not sure about this.

The Attempt at a Solution

You could do a whole lot of counting, but I don't think that's the point. Besides it would be a very tedious proces. I did it with a class of 1 and 2 students and counting even then took time.

 

[tiny-tim]

hi aaaa202!

(i haven't actually tried this , but …)

i think i'd calculate P_k, the probability that exactly k students out of 30 are absent

and then for each k the probability Q_k that less than one third of k from 30 come from the 10

(and then multiply and add)

 

[pasmith]

Homework Statement

In a class with 20 and one with 10 students each student has a probability of 0.3 to not show up on a particular day. On a given day, which class is most likely to have the highest ratio of absent students? This was in my exam, unfortunately I did not know how to do it.

Let N be the number of students absent from the large class, and M the number of students absent from the small class. The ratio of absent students will be larger for the large class if N > 2M, equal if N = 2M, and smaller if N < 2M. So you need to work out the probabilities of those three events.