25 people numbered 1 through 25 are assigned tasks 1 2 2

25 people, numbered 1 through 25, are assigned tasks 1, 2, . . . , 25 so that person 1 can only work on task 1, person 2 is equally likely to be assigned task 1 or 2, person 3 is equally likely to be assigned task 1, 2 or 3, · · · , and person 25 is equally likely to be assigned any of the tasks. Find (a) the expected number of tasks that no one does (b) the probability that every task has someone working on it

Solution

a)

the expected number of tasks that no one does is 0

because all 25 people are doing at least 1 task

b)

probability that every task has someone working on it = 25/25 =1

because you have 25 task and 25 people that will have those tasks