Question

Say you have 5 bins, and randomly throw 7 balls into them. 1. What is the probability that the first bin has precisely 3 balls in it? 2. What is the probability that the third bin has at least 3 balls in it? 3. What is the probability that at least one of the bins has precisely 3 balls in it?

Answer 1

Approach for first problem:

Number the bins and for i=1,2,3,4,5i=1,2,3,4,5 let BiBi denote the event that bin ii has precisely 33 balls in it.

Then to be found is:

P(⋃i=15Bi)P(⋃i=15Bi)

Applying inclusion/exclusion and symmetry we find that:

P(⋃i=15Bi)=5P(B1)−10P(B1∩B2)P(⋃i=15Bi)=5P(B1)−10P(B1∩B2)

How to find P(B1∪B2)P(B1∪B2)?

You do not need to find P(B1∪B2)P(B1∪B2)