Results 1 to 8 of 8

Math Help - A Probability problem

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    4

    A Probability problem

    There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after
    being defective. What is the probability that same musical sound would be produced 5 times
    consecutively?

    Please post the answer soon. I have doubt between 1/32 and 1/16

    Please post with explanation.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    If the toy is now defective, it has only two sounds to pick.

    Each time, the probability is 1/2 and since the question asks for 5 times, it simplies that you have:

    P(5\ times\ same\ sound) = \dfrac12 \times \dfrac12 \times\dfrac12 \times\dfrac12 \times\dfrac12= \left(\dfrac12\right)^5 = \dfrac{1}{32}

    EDIT: I forgot the second case, see below.
    Last edited by Unknown008; November 19th 2010 at 04:30 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    4
    Ok thanks a lot. But i have a doubt here.
    Lets take the two sounds to be named as 0 and 1
    so that the probable patterns are

    00000
    00001
    00010
    .
    .
    .
    .
    11110
    11111


    There are 32 pattern here.
    But patterns with same sound repeating five times is 00000,11111
    i.e. 2

    so isn't it 2/32=1/16??

    i know my explanation is somewhere wrong.
    But i can't get where i go wrong.
    Is it my understanding of the question wrong?? Or this is not the method??

    ex) Probability of getting same face in tossing a coin coin thrice is 2 out of 8 possibilities rite??

    isn't it similar??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Oh, duh, you're right. I didn't consider this. I'm a little tired, sorry for that.

    Let's say it like this.

    When the toy is defective, there are two sounds possible, 0 and 1 (using what you used)

    P(5\ times\ same\ sound) = P(5\ times\ 0) + P(5\ times\ 1) = \left(\dfrac12\right)^5 + \left(\dfrac12\right)^5 = \dfrac{1}{16}
    Follow Math Help Forum on Facebook and Google+

  5. #5

  6. #6
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    No, considering the problem well, the answer is indeed 1/16.

    You showed it yourself.

    1st link: Wrong
    2nd link: Wrong
    3rd link: Wrong (the person even concluded that the probability was 32!?)
    4th link: Wrong (this seems the same person in link 3)
    5th link: Wrong (uh... again the same person!?)

    1/16 is the right answer, let me assure you. You thought well
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2010
    Posts
    4
    Thanks a lot

    I had a huge doubt like how can be all the links wrong and i can be rite... Thanks a lot..

    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1
    Quote Originally Posted by sathishwizard View Post
    There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after being defective. What is the probability that same musical sound would be produced 5 times consecutively?
    That problem statement is really poorly written.
    I did not reply after I first read it for that reason.
    If we take it to mean one particular tune then the answer is \frac{1}{32}.
    If we take it to mean either of the remaining tunes then the answer is \frac{1}{16}.

    But why even mention the original ten tunes?
    It would make sense to ask “What is the probability that one particular tune of the original ten tunes, is played five consecutive after being disabled?”
    That is an interesting question.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: January 21st 2011, 11:47 AM
  2. Replies: 0
    Last Post: October 8th 2009, 08:45 AM
  3. another probability problem
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 28th 2008, 06:38 AM
  4. Probability problem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 10th 2008, 12:58 PM
  5. probability problem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 30th 2008, 06:58 PM

Search Tags


/mathhelpforum @mathhelpforum