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I have changed the 12 statements so that they are all true:
1. It is just as likely to be a day tomorrow, than there is to be a day after tomorrow.
2. In a school where there are more pupils than the days in that year, there will be two people who have the same birthday.
3. In a school where there is the same number of pupils than days in a year, and nobody is allowed to have the same birthday, it will be somebody’s birthday every day.
4. It is not possible to conclude that a randomly selected person from London will live to a longer age than a randomly selected person from Calcutta.
5. If everyone in the class rolled two fair dice until someone threw a double six, there would be at least one winner.
6. If I roll a die 100 times, it is impossible that all the numbers from one to six will be rolled an equal number of times.
7. If I flip a fair coin 20 times, there will be less than 21 heads thrown.
8. The mean, median and mode of a set of the same numbers always are the same.
9. The mean might not be less than both the median and the mode.
10. The student that got the lowest mark in a test didn’t get higher than the average mark.
11. Nobody scores higher than the average mark in a test where nobody got the same mark.
12. In a game where you can only score an even number of points (0, 2, 10 or 50), the average score over an odd number of games may be an even number.