Re: probability problem
Hello, jillgirl15!
Of the 15 members on a senate committee 10 plan to vote yes and 5 plan to vote no.
A reporter attempts to predict the outcome of the vote by questioning 6 senators.
Find the probability that 4 of the 6 senators plan to vote yes.
The reporter will randomly select 6 of the available 15 senators.
\(\displaystyle \;\;\)There are: \(\displaystyle \,\begin{pmatrix}15\\6\end{pmatrix} \,=\,5005\) possible selections.
To select 4 Yes from the available 10 Yes, there are \(\displaystyle \begin{pmatrix}10\\4\end{pmatrix}\,=\,210\) ways.
To select 2 No from the available 5 No, there are \(\displaystyle \begin{pmatrix}5\\2\end{pmatrix} \,= \,10\) ways.
\(\displaystyle \;\;\)Hence, there are \(\displaystyle 210\,\times\,10\:=\:2100\) ways to select 4 Yes and 2 No.
Therefore: \(\displaystyle \,P(\text{4 Yes & 2 No}) \:=\:\frac{2100}{5005} \:= \:\L\frac{60}{143}\)
