Results 1 to 2 of 2

Math Help - Probability Question!

  1. #1
    mattsh
    Guest

    Probability Question!

    Hi everyone,

    I need help on a probability question please. Thanks in advance. Here it is:

    1/3 of the people in a club are men.
    The number of men in the club is n.

    a) Write down an expression, in terms of n, for th enumber of people in the club.

    b) Two of the people in the club are chosen at random. The probability that both these people are men is one tenth. Calculate the number of people in the club.

    Thanks for any help!
    Matt
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by mattsh View Post
    Hi everyone,

    I need help on a probability question please. Thanks in advance. Here it is:

    1/3 of the people in a club are men.
    The number of men in the club is n.

    a) Write down an expression, in terms of n, for th enumber of people in the club.
    let P be the number of people in the club. 1/3 of the people in the club are men, so if n is the number of men:


    n = (1/3)P
    => P = 3n


    b) Two of the people in the club are chosen at random. The probability that both these people are men is one tenth. Calculate the number of people in the club.
    The probability of choosing one man is n/3n = 1/3, the probability of choosing the second man will be (n – 1)/(3n – 1) since after choosing one man, we have one less man in the group of men to choose from as well as one less person in the club in general to choose from. We want both these probabilities to happen at the same time, so we multiply them. So we have:


    1/3 * (n – 1)/(3n – 1) = 1/10 .........since 1/10 is the probability of these two events happening at the same time.


    => (n – 1)/(3n – 1) = 3/10
    => 10(n – 1) = 3(3n – 1) ...............cross multiplied
    => 10n – 10 = 9n – 3
    => n = 7 .....................................the number of men in the club


    => P = 3n = 3(7) = 21 ...................the number of people in the club.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: February 10th 2013, 03:11 PM
  2. Probability question involving (A given B type question )
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 9th 2009, 10:08 AM
  3. New Probability question
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 15th 2009, 07:50 AM
  4. probability question
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: May 16th 2009, 07:36 AM
  5. A probability question and an Expectations question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 29th 2006, 07:13 PM

Search Tags


/mathhelpforum @mathhelpforum