A computing center has 3 processors that receive n jobs, with the jobs assigned
to the processors purely at random so that all of the 3n possible assignments
are equally likely. Find the probability that exactly one processor has no jobs.
2007-02-03 16:31:55 · 2 answers · asked by Trivi 3 in Science & Mathematics ➔ Mathematics
The previous answer is almost correct, but he has overlooked the condition "exactly one". The solution he has given allows two processors being without jobs.
Let us call the processors A,B and C. The probability that C will not have any job = (2/3)^n. As mentioned above, this includes the possibility of A (or B) alone having all the jobs. The probability of A alone having all the jobs = (1/3)^n. The same is for B. So the probability of C alone not having any job = (2/3)^n - 2*(1/3)^n = (1/3)^n*(2^n-2). This of course can be for A or B also. So the answer is 3*(1/3)^n*(2^n-2)
2007-02-03 20:12:24 · answer #1 · answered by muten 2 · 3⤊ 0⤋
3c2*(2/3)^n=3*(2/3)^n
2007-02-03 16:41:02 · answer #2 · answered by bruinfan 7 · 0⤊ 0⤋