Results 1 to 2 of 2

Math Help - Probability

  1. #1
    Junior Member
    Joined
    Jul 2007
    Posts
    27

    Probability

    In a class there are 4 freshamn boys, 6 freshman girls and 6 sophomore boys. How many sophomore girls must be present if sex and class are to be independent when a student is selected at random?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,710
    Thanks
    629
    Hello, r7iris!

    In a class there are 4 freshman boys, 6 freshman girls and 6 sophomore boys.
    How many sophomore girls must be present if sex and class are to be independent
    when a student is selected at random?
    Two events, A and B, are independent if: . P(A \cap B) \;=\;P(A)\cdot P(B)

    Let x = number of sophomore girls.

    Tabulate the information:

    \begin{array}{cccccccc} & | & \text{Frosh} & | & \text{Soph} & | & \text{Total} & | \\ \hline<br />
\text{Boys} &|& 4 &|& 6 &|& 10 & |  \\ \hline<br />
\text{Girls} &|& 6 &|& x &|& x+6 & |  \\ \hline<br />
\text{Total} &|& 10 &|& x+6 &|& x+16 & |<br />
\end{array}


    We have: . P(\text{Boy}\cap\text{Frosh}) \:=\:\frac{4}{x+16}\qquad P(\text{Boy}) \:=\:\frac{10}{x+16} \qquad P(\text{Frosh}) \:=\:\frac{10}{x+16}

    If P(\text{Boy}) and P(\text{Frosh}) are independent,

    . . then: . P(\text{Boy}\cap\text{Frosh}) \;=\;P(\text{Boy})\cdot P(\text{Frosh})

    So we have: . \frac{4}{x+16} \;=\;\frac{10}{x+16}\cdot\frac{10}{x+16}

    Multiply by (x+16)^2\!:\;\;4(x+16) \:=\:100\quad\Rightarrow\quad x \,=\,9


    Therefore, there must be 9 sophomore girls.

    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: December 6th 2010, 04:57 PM
  3. Replies: 3
    Last Post: May 29th 2010, 07:29 AM
  4. Replies: 1
    Last Post: February 18th 2010, 01:54 AM
  5. Replies: 3
    Last Post: December 15th 2009, 06:30 AM

Search Tags


/mathhelpforum @mathhelpforum