Results 1 to 3 of 3

Thread: Work out this probability

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    28

    Exclamation Work out this probability

    "Write an expression for the probability that in a sequence of r random integers in the range [1,n] no integer occurs more than once"

    Is my answer right?

    Let the sequence be represented by $\displaystyle a_{n}= a_{1}, a_{2}, ... a_{r}$ where $\displaystyle r<=n$

    $\displaystyle P(a_{1}=a_{2}) = \frac{1}{n}$
    $\displaystyle P(a_{1}!=a_{2}) = 1-\frac{1}{n}$

    So $\displaystyle P(a_{1}!=a_{2}!=...!=a_{r}) = (1-\frac{1}{n})^r$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,782
    Thanks
    2824
    Awards
    1
    Quote Originally Posted by DaRush19 View Post
    "Write an expression for the probability that in a sequence of r random integers in the range [1,n] no integer occurs more than once"

    Is my answer right? No it is not.
    Let the sequence be represented by $\displaystyle a_{n}= a_{1}, a_{2}, ... a_{r}$ where $\displaystyle r<=n$
    $\displaystyle P(a_{1}=a_{2}) = \frac{1}{n}$
    $\displaystyle P(a_{1}!=a_{2}) = 1-\frac{1}{n}$
    So $\displaystyle P(a_{1}!=a_{2}!=...!=a_{r}) = (1-\frac{1}{n})^r$
    Here is a hint.
    Roll a die three times. The probability that no number occurs more than once is $\displaystyle \frac{6\cdot 5\cdot 4 }{6^3}$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2009
    Posts
    28
    Now that I've worked it out as $\displaystyle (n(n-1)(n-2)..(n-r+1))/n^r$ I'm stuck on when this is approximately equal to $\displaystyle 1/2$

    :S
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability question that I cant work out
    Posted in the Statistics Forum
    Replies: 3
    Last Post: Sep 27th 2011, 12:35 PM
  2. Replies: 1
    Last Post: Nov 23rd 2010, 02:45 AM
  3. Probability Please check my work!
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Jul 23rd 2009, 04:57 PM
  4. How can i work out this probability question?
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Nov 16th 2008, 10:00 AM
  5. probability and statictics work
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Apr 11th 2008, 04:12 PM

Search Tags


/mathhelpforum @mathhelpforum