Two events meeting

#1
Hello everyone,

I have a question regarding two events that take place randomly over a certain time period and meet. A similar problem would be phrased as follows, which is maybe simpler:

Person A and person B each have 20 balls labelled 1 to 20. Person A picks n number of balls and person B picks m number of balls. What is the probability that at least one number is picked by both persons? What is the probability that at least two numbers are picked by both players? What is the probability that exactly two numbers are picked by both players?

I have been thinking about this and made some progress in solving it but there is an error somewhere in my solution. Can someone please help me solve this or direct me to a reference where I will be able to solve this.

Thank you very much in advance for you help
Behrouz
 

hlsmith

Omega Contributor
#2
Let us see what you have so far. For clarification you can't return a ball after it is selected and you don't care about the order of the numbers selected, correct?
 
#3
Hi,
Thank you for your response. Yes you are correct. We don't put any balls back, and we don't care about any orders.
thank you
Behrouz
 
#5
For instance I can calculate the probability of both players picking a certain number. But I can't calculate the probability of both of them picking at least one same number.