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Liar Students (Posted on 2012-02-20) Difficulty: 1 of 5
There is a class of 7 students. Student 1 tells lie once a week. Student 2 tells lies twice a week and so on. Students 7 tells lies 7 times a week. A student will not lie more than once in a day. What is the probability that 7 students lie on the same day?

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Solution Two answers (spoiler) | Comment 1 of 2
It is not clear whether this question is being asked for a single day or for a week.

On any given day (where we have no information about what happened earlier in the week), the probability of all students lying = 
(1/7)*(2/7)*(3/7)*(4/7)*(5/7)*(6/7)*(7/7).

For a week, the probability that all students lie on a single day that week is (2/7)*(3/7)*(4/7)*(5/7)*(6/7)*(7/7).  This is arrived at by considering just the one day where student 1 lies.  This probability happens to be 7 times the first answer, but that is only because one of the students lies daily.

If Student 1 was not in the class, then figuring out the probability that all students lie on the same day at least once per week would not be a difficulty 1 problem.  Without doing it, I guess difficulty 2 or 3.

Edited on February 20, 2012, 6:16 pm
  Posted by Steve Herman on 2012-02-20 15:03:45

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