Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    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.
    Offline

    1
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    0
    ReputationRep:
    thankss
    Offline

    1
    ReputationRep:
    (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
    Offline

    0
    ReputationRep:
    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).
    Offline

    1
    ReputationRep:
    (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?
    Offline

    0
    ReputationRep:
    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.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (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!!:yes: hopefully stats exam went better than the C3 which was a bit of a disaster!
    Offline

    1
    ReputationRep:
    (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!!:yes: 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
    • Thread Starter
    Offline

    0
    ReputationRep:
    (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
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brexit voters: Do you stand by your vote?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.