I would like to ask a simple question that happened to me on an interview. The question was very simple and it was as follows:
We have 80 balls.
We have 4 random groups (each group will have 20 balls).
What is the probability of having the first 2 balls in the same group?
My answer was: 1/4 (0.25) because the first ball will go with probability 1 to whichever group. And the 2nd ball has 1/4 chances to join the same group as the 1st ball.
The answer they gave me was: 19/79 (=0.24)
Was my logic so wrong? I'm not sure how 19/79 really answers that the first 2 balls are in the same group.