A survey is being carried out to determine what fraction of Purdue students

use Purdue computers for personal (non-academic) purposes. Because some students

would be uncomfortable admitting to using Purdue computers for non-academic purposes, each person questioned is asked to roll a fair die in secret and answer NO if the

number "1" is shown, YES if the number "6" is shown, but to truthfully answer YES

or NO if "2", "3", "4", or "5" are shown on the die. Because the outcome of the die

is not revealed, it is impossible to tell from the answer given whether or not a student

actually uses Purdue computers for non-academic reasons.

Suppose that the probability that a student answers YES in this survey is found to

be 2/3.

(a) What is the true probability that a student uses Purdue computers for nonacademic reasons?

(b) How likely is it that a student who answered YES in the survey actually uses

Purdue computers for non-academic reasons?

(c) How likely is it that a student who answered NO in the survey actually uses

Purdue computers for non-academic reasons?