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1. It is just as likely to rain tomorrow as it is to rain the day after tomorrow.
Usually true, because the clouds remain the day after tomorrow. However this depends on wind speed and direction.
2. In a school, there will be two people who share a birthday.
Usually true as there are usually over 365 pupils in one school. So the chances are much greater. However if the school only has 50 students this will be much more unlikely
3. In a school, it will be someone's birthday every day.
Sometimes true. As many people could share the same birthday. So not all the birthdays will be covered.
4. A randomly selected person from London will live to a greater age than a randomly selected person from Calcutta.
Usually true as the living conditions in London are greater on average than those in Calcutta. However there are rich people in Calcutta who could afford greater healthcare than people in London.
5. If everyone in the class rolled two dice until someone threw a double six, there would be one winner.
Always true because the game stops when someone throws a double six not when we run out of people.
6. If I roll a die 100 times, I will get about the same number of 1s as 6s.
Almost always true as there is a 1/6 theoretical probability for each side, however the real value is affected by human error.
7. If I flip a fair coin 20 times, I will get 10 heads.
Usually true as the theoretical probability is ½ for heads and tails however the way you flip the coin affects the outcome leading to slightly different results.
8. The mean, median and mode of a set of numbers can't all be the same.
Almost never true as they measure different things so they can have the same outcome e.g. 1,1,1,1,1 has the same mean, median and mode, so this statement is false.
9. The mean cannot be less than both the median and the mode.
Almost always true as the median is the middle value and the mode which is the most popular influences the outcome of the mean e.g. 1,1,1,1,1 has a mean median and mode of 1, so the mean is not lower.
10. Half of the students taking a test score less than the average mark.
Not always true as if they use the mode and most people score highly the average will be high. However if they use the mean it is more likely and if they use median it will always be true
11. Nobody scores higher than the average mark in a test.
Almost never true unless everyone gets the same mark. As to calculate the median you need values higher than the average. If the mode is the highest mark then this is true, but only then. Also for the mean the value is almost never the highest.
12. In a game where you can only score an even number of points (0, 2, 10 or 50), the average score over a series of games must be an even number.
Not always true as if there are 3 games played and someone score 4, 12 and 6 you would not get an even number as the result is not divisible by 3.