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Math Help - Probability question.

  1. #1
    Junior Member
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    Probability question.

    Hi could any one help me with the following question please.

    A poll is carried out in the run up to a general election which give the following results:

    Age Group---Conservatives---Labour---Liberal Democrats---Others

    18-34--------32.7%----------30.7%-----------29.0%------7.6%
    35-64--------35.5%----------28.9%-----------24.8%------10.8%
    65+ ---------43.9%----------31.0%-----------16.0%------9.1%

    The age groups represented are:

    18-34-------35-64------65+

    21.9%-------54.1%-----24.0%

    (a) Find the probability that a randomly chosen voter who takes part in the poll but whose age is not know voted Conservative.
    (b) Suppose the voter did vote Conservative, find the probability that he/she is at least 65 years old.


    I think for (b) you would use the conditional probability formula but how would (a) be calculated?
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  2. #2
    Super Member

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    Hello, axa121!

    A poll is carried out prior to a general election which give the following results:

    . . \begin{array}{|c|c|c|c|c||c|}<br />
\text{Ages} & \text{Cons.} & \text{Labor} & \text{Lib.Dem.} & \text{Others} & \text{Total} \\ \hline \hline<br /> <br />
18-34 & 32.7\% & 30.7\% & 29.0\% & 7.6\% & 21.9\% \\ \hline<br />
35-64 & 35.5\% & 28.9\% & 24.8\% & 10.8\% & 54.1\% \\ \hline<br /> <br />
65+ & 43.9\% & 31.0\% & 16.0\% & 9.1\% & 24.0\% \\ \hline \end{array}

    (a) Find the probability that a randomly chosen voter who takes part in the poll
    but whose age is not known voted Conservative.

    A more complete table looks like this:

    . . \begin{array}{|c|c|c|c|c||c|}<br />
\text{Ages} & \text{Cons.} & \text{Lab.} & \text{Lib.Dem.} & \text{Others} & \text{Total} \\ \hline \hline<br /> <br />
\text{18-34} & 0.071613 & 0.007233 & 0.063510 & 0.016644 & 0.219 \\ \hline<br /> <br />
\text{35-64} & 0.192055 & 0.156349 & 0.134168 & 0.058428 & 0.541 \\ \hline<br /> <br />
\text{65+} & 0.105360 & 0.074400 & 0.038400 & 0.021840 & 0.240 \\ \hline\hline<br />
\text{Total} & 0.369028 & 0.297982 & 0.236078 & 0.096912 & 1.000 \\ \hline<br />
\end{array}


    P(\text{Cons.}) \:=\:0.369028




    (b) Suppose the voter did vote Conservative.
    Find the probability that he/she is at least 65 years old.

    P(\text{(65+)}\,|\,\text{(Cons)}) \;=\;\dfrac{P(\text{(65+)} \wedge \text{(Cons)})}{P(\text{Cons})} \;=\;\dfrac{0.105360}{0.369028} \;=\;0.285506791
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  3. #3
    Junior Member
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    Ah thanks. I was trying something completely different.
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