Results 1 to 3 of 3

Math Help - probability of picking A.P series.

  1. #1
    Member
    Joined
    Feb 2010
    From
    in the 4th dimension....
    Posts
    122
    Thanks
    9

    probability of picking A.P series.

    Out of 21 tickets marked with numbers from 1 to 21, three are
    drawn at random. Find the probability that the numbers on them are in Arithmetic Progression?


    I can understand that there are C(21,3) outcomes.But how many A.P series can be there?
    Last edited by mr fantastic; December 7th 2011 at 02:20 AM. Reason: Merged posts.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: probability of picking A.P series.

    Quote Originally Posted by earthboy View Post
    Out of 21 tickets marked with numbers from 1 to 21, three are
    drawn at random. Find the probability that the numbers on them are in Arithmetic Progression?


    I can understand that there are C(21,3) outcomes.But how many A.P series can be there?
    Think about how many arithmetic progressions are possible ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,676
    Thanks
    608

    Re: probability of picking A.P series.

    Hello, earthboy!

    Out of 21 tickets marked with numbers from 1 to 21, three are drawn at random.
    Find the probability that the numbers on them are in Arithmetic Progression


    I can understand that there are C(21,3) outcomes.
    But how many A.P series can be there?

    There is no formula for your question.

    I see no choice but to List them and Count them . . . and look for a pattern.

    Sequences beginning with 1: . \begin{Bmatrix}1,2,3 \\ 1,3,5 \\ 1,4,7 \\ 1,5,9 \\ \vdots \\ 1,10,19 \\ 1,11,21 \end{Bmatrix}

    Sequences beginning with 2: . \begin{Bmatrix}2,3,4 \\ 2,4,6 \\ 2,5,8 \\ 2,6,10 \\ \vdots \\ 2,11,20 \end{Bmatrix}

    Sequences beginning with 3: . \begin{Bmatrix}3,4,5 \\ 3,5,7 \\ 3,6,9 \\ 3,7,11 \\ \vdots \\ 3,12,21 \end{Bmatrix}

    . . . . . . . . . . . . . . . . . . . . . . . . . . \vdots

    Sequences beginning with 17:. \begin{Bmatrix}17,18,19 \\ 17,19,21\end{Bmatrix}

    Sequences beginning with 18:. \begin{Bmatrix}18,19,20\end{Bmatrix}

    Sequences beginning with 19:. \begin{Bmatrix}19,20,21\end{Bmatrix}


    Do you see a pattern?

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Picking Marbles from a bag--Probability
    Posted in the Statistics Forum
    Replies: 5
    Last Post: February 24th 2011, 05:51 PM
  2. Probability: Picking M&M's
    Posted in the Statistics Forum
    Replies: 6
    Last Post: October 13th 2010, 05:54 AM
  3. Probability picking a number in an infinite set?
    Posted in the Advanced Statistics Forum
    Replies: 12
    Last Post: August 17th 2009, 02:07 AM
  4. probability of picking a ball (this is easy :P)
    Posted in the Statistics Forum
    Replies: 3
    Last Post: May 2nd 2009, 07:57 AM
  5. probability of picking at least one
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 22nd 2007, 04:27 PM

Search Tags


/mathhelpforum @mathhelpforum