1.It is just as likely to rain tomorrow as it is to rain the day after tomorrow.
This statement is true if you have no data on the chances of rain for tommorrow or the next day, but if you have the data then the probability would correspond to that and the chance would be different for each
2.In a school, there will be two people who share a birthday.
There is obviously a probability of their being a sahred birthday, but it will not always happen, again it depends on whether there are two people who share a birthday in the school and how many people there are in the school, it also depends on what month it is as more people would be born in a certain month e.g. September
3.In a school, it will be someone's birthday every day.
Similar to the last statement it depends if their are enough people in the school for there to be a birthday everyday, if you have enough then there is a possibility but it will not be definite.
4.A randomly selected person from London will live to a greater age than a randomly selected person from Calcutta.
Statistically this should be the cse as peopl in London have a greater life expectancy then those in Calcutta, but as always there is always the probablility that a drug addict or a person with a terminal illnes will be selected from London and a very fit and healthy individual will b picked from Calcutta
5.If everyone in the class rolled two dice until someone threw a double six, there would be one winner.
This woukld definitely be true because if they took turns and only one person rolled two dice per turn then as soon as someone got 12 the game would end only allowing one person the oppotuninty, if more then one person was rolling the dice at the same time then there could be more then one winner, if they both rolled it at the same time.
6. If I roll a die 100 times, I will get about the same number of 1s as 6s.
This could happen and is statistically possible but it is not assured as it is possible to roll only sixes which would result in 100 sixes to 0 ones.
7.If I flip a fair coin 20 times, I will get 10 heads.
This is what we would expect due to the probablity but as it is possible to flip 20 heads and no tails then it will not always happen.
8.The mean, median and mode of a set of numbers can't all be the same.
It is possible to have them all the same, for example if the numbers were 1,1,2,2,2,3,3 then the mean would be two the median would be two and the mode would be two, but it is more likely that the mode, median and mean will be different.
9.The mean cannot be less than both the median and the mode.
This is likely but not always right because if all the numbers are the same but the one on the ned duobled then the mean is likely to be less tyhen both the median and the mode, there are also other circumstances e.g
1,2,3,4,5,6,6,6,7,8,9,10
mode = 6
median = 6
mean = 5.83
10.Half of the students taking a test score less than the average mark.
like most of the others this is possible both ways, it is possible for their to be more students with a mark below or above the average mark but only if someone gets a very low or very high mark.
11.Nobody scores higher than the average mark in a test.
This is very unlikly but is still possible if every one gets exactly the same mark, this would result in no-one being above or below the average mark.
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.
If there are you get a score less then or equal to the number of rounds then it is possible to get an odd number e.g. 2 ponts out of 2 rounds results in an average of 1. it is also possible to get an average even score e.g. 4 out of 2 rounds equals an average score of 2.