Probability of Having One Person in Your Class

Question

If there are 2,945 people at a school and there are 6 periods with 35 people in each class, what is the probability of one specific person person being in my class?

Answer 1

The probability of one specific person to be in at least one of your 6 classes is 1- probability of one specific person to be in none of your classes.

What is the probability that the specific person will not be in your first class? Well you can have any combination of 35 people from the remaining 2944 so that is 2944C35.

The probability for 6 classes, assuming the classes are independent is (2944C35)^6

Thus the probability of one specific person to be in at least one of y our 6 classes is 1-(2944C35)^6.

Note important assumptions here are that each of the students is equally likely to be in a class and that the classes are completely independent. in reality, out of 2945 very few are say ready for Calculus and those who take Calculus are likely also taking an advanced science class, etc.

Note: nCk=n!/[k!(n-k)!]