Probability With replacement A bag contains blue, red and white discs. In an experiment, 24 students in a class take turns to remove a disc from the bag, record its colour and replace it. This is repeated 10 times. At the end of the experiment the relative frequencies are:
Red: 118/240, blue: 83/240, white: 39/240
Anne suggests that there are 10 discs in the bag. Is this a reasonable suggestion?
Based on the information, how many discs of each colour do you think are in the bag? 
 A: Firstly I agree with John Chessant in the sense of the ratio of the various coloured discs, i.e. R:B:W = 3:2:1.
As to whether Anne's suggestion is "reasonable" or not, there  is a somewhat subjective element to this question.
I'm inclined to think that Anne must of had some prompting factor to suggest 10, she may have gave such a number because she could clutch all or most of the discs in the one hand thereby giving her a fair guesstament as to the number of discs.
 A statistician would deem it blatantly unreasonable, Anne's mother would deem it highly reasonable. I waver somewhere in between, after all it is not outside the realm of possibilities that the results can occur with the ratios of 5:3:2 however unlikely. But personally believing the ratio is most likely 3:2:1 with the actual numbers being 6,4,2, for Red, Blue and White respectively, then Anne's guesstament is out by only 2, if this is the case I still hold the same view regarding her suggestion i.e. Not unreasonable ( call me a softie).
In light of what I have said in the above I give my answer to the second question as----
Red=6
Blue=4
White=2
A: I think that $10$ discs is not a reasonable suggestion. It is most likely to be a multiple of $6$. In that case, there would be $3n$ red discs, $2n$ blue discs, and $n$ white discs, for a total of $6n$ discs.
To see why, notice that since $240$ discs were recorded, the numerators give the number of times each disc was chosen (i.e., $118$ red, $83$ blue, and $39$ white). Notice that these are about a $3:2:1$ ratio! (One way to see this is to estimate $118\to 120$, $83\to80$, and $39\to40$.)
So the number of red discs is three times the number of white discs, and the number of blue discs is two times the number of white discs.
(Edit: Of course, it is possible that, given $10$ discs, the recorded numbers of discs would still be as above, but it is extremely unlikely.)
