The math teacher from season 1 did the math wrong (explanation)
In the series, the math teacher had 15 pairs of glasses ahead of him. To understand it better, let's pretend that there were only 2 pairs ahead. In this case, it seems logical to think that the probability of succeeding in both cases is 1/4, but this assumes the possibility that one can fail in both the first case and the second, but this is logically impossible. If you fail the first glass, you are already dead, so that possibility does not exist.
In fact, there are only three possibilities: to fail on the first glass, to not fail on the first but fail on the second, and to fail on neither. Therefore, the probability of getting it right both times is 1/3. You can try to imagine in your head all the possibilities if there are three pairs of glasses or more and you will quickly realize what's the pattern: if the number of pairs of glasses is n, the number of possibilities is n+1.
In the situation of the math teacher: he had 15 pairs of glasses, therefore the probability of getting it right 15 times is much greater than 1 in 2 to the 15th: it is 1 in 16 (wow!). He actually managed to succeed three times. The likelihood of that happening is also far better than 1 in 2 to the 3rd (which would be 1 in 8), it was actually 1 in 4. And the likelihood of him getting to the 4th glass was 1 in 5.
Idk if anyone noticed this before but lol
In the series, the math teacher had 15 pairs of glasses ahead of him. To understand it better, let's pretend that there were only 2 pairs ahead. In this case, it seems logical to think that the probability of succeeding in both cases is 1/4, but this assumes the possibility that one can fail in both the first case and the second, but this is logically impossible. If you fail the first glass, you are already dead, so that possibility does not exist.
In fact, there are only three possibilities: to fail on the first glass, to not fail on the first but fail on the second, and to fail on neither. Therefore, the probability of getting it right both times is 1/3. You can try to imagine in your head all the possibilities if there are three pairs of glasses or more and you will quickly realize what's the pattern: if the number of pairs of glasses is n, the number of possibilities is n+1.
In the situation of the math teacher: he had 15 pairs of glasses, therefore the probability of getting it right 15 times is much greater than 1 in 2 to the 15th: it is 1 in 16 (wow!). He actually managed to succeed three times. The likelihood of that happening is also far better than 1 in 2 to the 3rd (which would be 1 in 8), it was actually 1 in 4. And the likelihood of him getting to the 4th glass was 1 in 5.
Idk if anyone noticed this before but lol