Results 1 to 7 of 7

Math Help - Probability of rolling a single die and getting a 5 in fewer then 4 rolls.

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    6

    Probability of rolling a single die and getting a 5 in fewer then 4 rolls.

    I am having trouble with this problem......

    Find the probability of rolling a single die and getting a 5 in fewer then 4 rolls.
    (You stop when you get a 5 )


    Thanks in advance
    Last edited by mr fantastic; June 21st 2011 at 09:30 PM. Reason: Re-titled.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2

    Re: probability

    1st roll - 5 (1/6) or not a 5 (5/6)
    2nd roll (5/6) - 5 (1/6) or not a 5 (5/6)
    3rd roll (5/6)^2 - 5 (1/6) or not a 5 (5/6)
    4th roll (5/6)^3 - 5 (1/6) or not a 5 (5/6)
    5th roll (5/6)^4 - 5 (1/6) or not a 5 (5/6)

    You decide where to stop and what it all means.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2011
    Posts
    6

    Re: probability

    So I would stop at the third roll because it is less then 4 and it means that the probability is (5/6)^2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2

    Re: probability

    Good try, but no.

    P(5 on 1st roll) = 1/6
    p(5 on 2nd roll) = (5/6)*(1/6)
    p(5 on 3nd roll) = [(5/6)^2]*(1/6)

    You must convince yourself that we have the whole distribution. If we keep rolling, do all the probabilities sum to unity?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2011
    Posts
    6

    Re: probability

    so I have to add roll 1, 2 and 3 in order to get the probability of rolling a 5 under 4 rolls so it would be [(5/6)^2]*(1/6)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2

    Re: probability

    No, that's just roll 3. You might hit it on either roll 1 or roll 2.

    1/6 + (5/6)*(1/6) + [(5/6)^2]*(1/6)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Oct 2010
    From
    Johor Bahru
    Posts
    27

    Re: Probability of rolling a single die and getting a 5 in fewer then 4 rolls.

    Quote Originally Posted by aprinzen View Post
    I am having trouble with this problem......

    Find the probability of rolling a single die and getting a 5 in fewer then 4 rolls.
    (You stop when you get a 5 )


    Thanks in advance
    What you're looking for is the probability of getting a number '5' in less than 4 toses.

    So that means there's only toss 1, toss2, toss 3.

    For toss 1, P(5 on 1st roll) = 1/6
    For toss 2, p(5 on 2nd roll) = (5/6)x(1/6)
    For toss 3, p(5 on 3nd roll) = [(5/6)^2]x(1/6)

    Since it's less than 4 toses, remember that you need to COUNT IN ALL THE FIRST 3 ROLLS.

    THEN, you'll get 1/6 + (5/6)x(1/6) + [(5/6)^2]x(1/6) = 91/216

    Okay?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. probability of rolling a die...
    Posted in the Statistics Forum
    Replies: 5
    Last Post: April 17th 2011, 06:52 AM
  2. Replies: 3
    Last Post: October 19th 2010, 04:49 AM
  3. probability of rolling a die
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 25th 2009, 08:05 PM
  4. Probability--Rolling a die
    Posted in the Statistics Forum
    Replies: 4
    Last Post: August 29th 2009, 06:04 PM
  5. probability: rolling a die
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 21st 2007, 11:02 AM

Search Tags


/mathhelpforum @mathhelpforum