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

    9
    ReputationRep:
    This is from Siklos' book.

    My question is about part (i): I just did it by saying that 1 of the keys has to be the correct one so therefore the probability must be 1/k, since each key is equally likely of being anywhere in the chain and there are k keys in total.

    However I don't understand the solution given by the author. Specifically I don't understand where the product given for 2 \le n \le k comes from? Can someone please explain this part?
    Attached Images
      
    • Study Helper
    Offline

    13
    (Original post by FXLander)
    This is from Siklos' book.

    My question is about part (i): I just did it by saying that 1 of the keys has to be the correct one so therefore the probability must be 1/k, since each key is equally likely of being anywhere in the chain and there are k keys in total.

    However I don't understand the solution given by the author. Specifically I don't understand where the product given for 2 \le n \le k comes from? Can someone please explain this part?
    You'll kick yourself.

    It comes from the line above.

    E.g. to succeed on the third attempt, requires it to fail on the first and fail on the second.

    P(fail on first) = (k-1)/k

    k-1 keys left to try:

    P(fail on second) = (k-2)/(k-1)

    k-2 keys left.

    P(succeed on third) = 1/(k-2)
 
 
 
  • 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
    Will you be richer or poorer than your parents?
    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

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