Workers 1 n are currently idle Suppose that each worker

Workers 1, . . . , n are currently idle. Suppose that each worker, independently, has probability p of being eligible for a job, and that a job is equally likely to be assigned to any of the workers that are eligible for it (if none are eligible, the job is rejected). Find the probability that the next job is assigned to worker 1.

Solution

first the worker 1 has to be selected

probability for it = 1/n ( since there are n workers)

later he has to be proven eligible

probability for it is p ( given)

so net required probability = 1/n * p = p/n