5/3. We have 12 boxes and 24 balls. We place the balls into the boxes one...

Transcribed Image Text:

5/3. We have 12 boxes and 24 balls. We place the balls into the boxes one by one. For every ball, independently of the others, we choose where to place it uniformly at random.. (a) Calculate the probability that there will be exactly 2 balls in every box. (b) Denote by X the number of boxes containing exactly 2 balls. Calculate the expected value of X. 5/3. We have 12 boxes and 24 balls. We place the balls into the boxes one by one. For every ball, independently of the others, we choose where to place it uniformly at random.. (a) Calculate the probability that there will be exactly 2 balls in every box. (b) Denote by X the number of boxes containing exactly 2 balls. Calculate the expected value of X.