The document presents a probability problem involving two boxes of balls, one containing 10 balls and the other 100 balls. It asks for the probability that a randomly chosen ball numbered 5 came from the first box and also seeks to calculate this probability if all balls are mixed together. The problem requires understanding conditional probabilities and is framed in a mathematical context.

1. We have two same boxes. One box has 10 balls numbered 1 to 10 and another one has 100 balls
numbered 1 to 100. You first pick a box at random, then pick a ball at random, and the balls
number is 5 (exactly 5, not a number including 5).
(a) What is the probability that it came from the first box?
(b) If we mix all 110 balls and randomly choose a ball. The balls number is 5. What is the
probability in (a)?