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?
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
Two answers (spoiler)
