2 ms·
That formula is missing something because for over 100 students the teacher can't lose. (they get over 100 guesses and there are only 100 numbers possible)
by aidenn0 3y ago
That formula is missing something because for over 100 students the teacher can't lose. (they get over 100 guesses and there are only 100 numbers possible)
- mewpmewp2 3y agoIf the teacher does have 100 guesses then they wouldn't lose right. Then it would be 1 to the power of 100. I guess I should've clarified that the 0.3 refers to being able to choose 30 out of 100 numbers?
- svat 3y agoMore precisely, if there are N students, the probability is (min(N,100)/100)^N. This is 1 for N ≥ 100. And the probability at N=30 is indeed a tiny 2e-16, which shows that the children's "random" picks were far from uniformly random. (Incidentally, even with N=99 the probability is 0.37 ≈ 1/e, and the probability is lowest at N=37 ≈ 100/e. This is not a coincidence.)