Probability of two people sitting at the same table.

Question

Let’s say that there are 20 people and 5 tables with 4 chairs at each table. Each person is assigned a seat at random. 2 of the people are friends. What is the probability that the 2 friends will sit at the same table?

Answer 1

Hey, Tyler,

Okay, so we have 5 tables, and we want two friends out of the 20 to sit at the same table. To do this, let's just say that it is Table #1 out of 5.

The probability of Friend A sitting there is 4/20 or 1/5.

Now that Friend A is seated, one of the seats is unavailable to friend B. He only has 3 seats at Table #1 out of a total of 19 seats. So the probability of him sitting at the same table is 3/19

Since it doesn't matter which table they both sit at (as long as they both sit at the same one, the second number is what we are looking for. The answer is 3/19 or ~15.8%.

Hope this helps!