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# S2 problem.. watch

1. I went through the past papers..
came across this question and have no idea how to work it out.. and i dont really follow the mark scheme

here it is:
A bag contains a large number of coins:
75% are 10p and 25% are 5p
A random sample of 3 coins is drawn from the bag.
Find the sampling distribution for the median of the values of the 3 selected coins.
2. (Original post by celinex)
I went through the past papers..
came across this question and have no idea how to work it out.. and i dont really follow the mark scheme

here it is:
A bag contains a large number of coins:
75% are 10p and 25% are 5p
A random sample of 3 coins is drawn from the bag.
Find the sampling distribution for the median of the values of the 3 selected coins.
Essentially, you are looking at all the different probabilities involved in getting 5 or 10 as the median to produce a sampling distribution.

Now you know that there are only 8 ways of getting 3 coins using only 5p and 10p coins

(10,10,10)
(10,10,5)
(10,5,10)
(5,10,10)

(5,5,5)
(5,5,10)
(5,10,5)
(10,5,5)

The first four have a median of 10. The second four have a median of 5. You want to find the probability of getting 5 and 10 as your median so you just calculate the probability of getting 10 which is the individual probabilities of the first four added together and then find the probability of getting a median of 5 i.e. (1 - p(10)) or you can work out the individual probabilities and add like before

The first list.
Probability of getting 10,10,10 is (.75)^3
Probability of getting 10,10,5 is 3C2 (.75)^2(.25)

Add that together you should get .84375.
3. thankss
4. (Original post by celinex)
thankss
My pleasure, I do admit, they could have just used mode instead of median in that example to make the question less ambigious. just PM if you need any more help
5. The mark scheme for this question is glorious: you get 4, count 'em, 4 marks for listing all the possible cases. Then like 3 for the standard probability stuffs.

The fact that they used median makes it even easier, because there's no messy fraction: there's literally two possible values which median can be.

I did a tree diagram: it's unneccessary but helps you understand it fully (it did me).
6. (Original post by Salavant)
The mark scheme for this question is glorious: you get 4, count 'em, 4 marks for listing all the possible cases. Then like 3 for the standard probability stuffs.

The fact that they used median makes it even easier, because there's no messy fraction: there's literally two possible values which median can be.

I did a tree diagram: it's unneccessary but helps you understand it fully (it did me).
Ya, I said mode, not mean, so there wouldn't have been any messy fractions anyway. It's just the phrasing of the question that might have thrown some people off. A tree diagram? That's Long! even for this small case, I always find tree diagrams end up messy because you don't leave enough space further down the branches. Congratus on your cambridge offer, what college?
7. Mode is for sillies. It's kinda dull. But yeah, same result, I can't read the Englishes it seems :P.

I love tree diagrams: they are so pretty. I'm kinda good at leaving space as well: there's a knack to it. It's gloriously pointless here though.

Hmm, does it not say? Gonna fix that. Emmanuel, regardless.
8. (Original post by Clarity Incognito)
My pleasure, I do admit, they could have just used mode instead of median in that example to make the question less ambigious. just PM if you need any more help
i cant thank you enough!! in the exam few days ago a question like this came up.. but to do with the mean i understood what they wanted to doo hehe but lol i dnt no if got it right but still thanks soooo much!! hopefully stats exam went better than the C3 which was a bit of a disaster!
9. (Original post by celinex)
i cant thank you enough!! in the exam few days ago a question like this came up.. but to do with the mean i understood what they wanted to doo hehe but lol i dnt no if got it right but still thanks soooo much!! hopefully stats exam went better than the C3 which was a bit of a disaster!
ahahaha yeah, the question had exactly the same layout, there's actually the S2 thread which I've posted on and a guy put up the paper and answers, you can go check it out and see how you did. C3 was a tricky paper but that means the grade boundaries will be lower and everything, I thought I did pretty good, aiming high lolz
10. (Original post by Clarity Incognito)
ahahaha yeah, the question had exactly the same layout, there's actually the S2 thread which I've posted on and a guy put up the paper and answers, you can go check it out and see how you did. C3 was a tricky paper but that means the grade boundaries will be lower and everything, I thought I did pretty good, aiming high lolz
kk will check the mark scheme out
yeah.. nd i was aiming for an A* in maths.. tho im not sure its possible now, considering how hard i found C3 lol

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