Results 1 to 3 of 3

Math Help - Help with Simple Probability Program

  1. #1
    november7
    Guest

    Help with Simple Probability Program

    This probably isn't that difficult of a problem for most of you, but I am stuck on it. Can anyone help?

    Question: What is the minimum number of times you must roll a number cube to have a 50% chance of getting a 6.

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by november7 View Post
    This probably isn't that difficult of a problem for most of you, but I am stuck on it. Can anyone help?

    Question: What is the minimum number of times you must roll a number cube to have a 50% chance of getting a 6.

    Thanks in advance!
    The probability that you get no six on first roll is 5/6. The probability that you get no sixes on two rolls is (5/6)(5/6). And in general the probability that you get no sixes on n rolls is (5/6)^n. Now if n=3 then that number is .578 (thus it is likely you get no sixes on 3 rolls), and if n=4 then that number is .482. Thus, it is unlikely to get no sixes after 4 rolls. That number is 4.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,719
    Thanks
    635
    Hello, november7!

    Same solution, different spin . . .


    What is the minimum number of times you must roll a number cube
    to have a 50% chance of getting a 6. ?

    Consider rolling the die n times and not getting a 6.

    The probability of getting a number other than 6 is: \frac{5}{6}
    Then: . P(\text{no 6 in }n\text{ rolls}) \;=\;\left(\frac{5}{6}\right)^n
    And we want this probability to be less than 50%.

    So we have . \left(\frac{5}{6}\right)^n \:<\:0.5

    Take logs: . \ln\left(\frac{5}{6}\right)^n \:<\:\ln(0.5)\quad\Rightarrow\quad n\cdot\ln\left(\frac{5}{6}\right) \:<\:\ln(0.5)


    Divide by \ln\left(\frac{5}{6}\right) . . . a negative quantity.
    . . n \:> \:\frac{\ln(0.5)}{\ln\left(\frac{5}{6}\right)} \;=\;3.801784017

    Therefore, we must roll at least 4 times.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: May 27th 2011, 01:08 PM
  2. Simple Math Program
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 4th 2009, 06:17 PM
  3. Fixing The Program (Program Correctness)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 21st 2009, 02:17 PM
  4. Simple program for quizing basic math skills
    Posted in the Math Software Forum
    Replies: 0
    Last Post: July 25th 2008, 09:52 PM
  5. Simple probability
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 19th 2007, 04:16 PM

Search Tags


/mathhelpforum @mathhelpforum