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Guessing alphabet letters with order

  1. Oct 27, 2011 #1
    We need to guess 5 letter among alphabet of A~Z. What is probability of correctly guessing 2, 3, 5 letters respectively. given they are all upper letters and alphabetic order is preserved (no Z comes before any letter, or no A comes after any letter etc).

    I know mentioned it before, but I really appreciate providing any way of solving the problem. I really need to solve the problem.. please help!!!!!!!!!!!!
    Thanks in advance for you thoughts shared.
     
  2. jcsd
  3. Oct 27, 2011 #2

    DaveC426913

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    Gold Member

    You need to show your efforts before we can help. What ideas have you thought of so far?


    Start wit the simplest case. What is the probability of guessing 1 letter correctly?
     
  4. Oct 28, 2011 #3
    Thanks for your attention.
    Analysis:
    1st, Sample space: there are 26 letters and each of them can be filled up and thus sample space is 26*26*26*26*26=26^5.
    2nd, let`s restrict that first letter (FL) must be one of 'A~V' (the order of 5 correct letters is same as the order of 'A~Z'), thus P(FL)=1/21. Second letter(SL) would be, if FL is 'A', is one of 'B~W', thus P(SL)=1/21 as well. But if FL is 'C', SL is one of 'C~W', thus P(SL)=1/20 . Once FL is 'D','E','F'.... , then P(SL)=1/19,1/18,1/17 respectively.....Thus, P(SL)=1/21+1/20.... Third Letter is........This is long calculation, but I was wondering if there is any alternative way doing that....
    Please feel free to offer your suggentions.
    Thanks again for sharing ideas!!!!
     
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