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Math Help - Probibality problem, Pls help

  1. #1
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    Probibality problem, Pls help

    A market research study is being conducted to determine if a product modification will be well received by the public. A total of 910 consumers are questioned regarding this product. The table below provides information regarding this sample.

    _______Positive Reaction.....Neutral Reaction.....Negative Reaction
    Male............190....................70......... .................110
    Female..........210...................200......... ................130

    (a) What is the probability that a randomly selected male would find this change unfavorable (negative)?
    (b) What is the probability that a randomly selected person would be a female who had a positive reaction?
    (c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male?
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  2. #2
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    Quote Originally Posted by stoorrey View Post
    (a) What is the probability that a randomly selected male would find this change unfavorable (negative)?
    = number on males with negative reaction divided by the total number of males


    Quote Originally Posted by stoorrey View Post
    (b) What is the probability that a randomly selected person would be a female who had a positive reaction?
    = number of females with a positive reaction divided by the total number of people



    Quote Originally Posted by stoorrey View Post
    (c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male?

    This is conditional probabilty, let A be the person with a negative reaction and B be a male

    You require P(B/A) = \frac{P(A\cap B)}{P(A)}
    Last edited by pickslides; December 22nd 2009 at 01:50 PM. Reason: bad latex
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  3. #3
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    Thanks a lot

    Thanks a lot for your help pickslides

    but pls can you elaborate part c a bit more

    i dont know how to use the formula.
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  4. #4
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     P(B/A) = \frac{P(A\cap B)}{P(A)}

    = (number of males with a negative reaction divided by total number of people in the survey) divided by (number of people (males + females) with a negative reaction divided by total number of people in the survey)
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  5. #5
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    Quote Originally Posted by pickslides View Post
     P(B/A) = \frac{P(A\cap B)}{P(A)}

    = (number of males with a negative reaction divided by total number of people in the survey) divided by (number of people (males + females) with a negative reaction divided by total number of people in the survey)
    Doesn't a condition alter the sample space? So shouldn't the answer be:

    (number of males with a negative reaction)/(total number of people with a negative reaction)

    The math works out the same way as in your solution, however your logic intrigues me.
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  6. #6
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    You are correct to say the arithmetic will give the same solution. My explanation is from the definition in the equation supplied. Yours is a simplification knowing the number of total people surveyed will cancel out.
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  7. #7
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    Hello, stoorrey!

    pickslides is absolutely correct.
    Vitruvian's approach to part (c) is also correct and more direct.


    A market research study is being conducted to determine if a product modification
    will be well received by the public.
    A total of 980 consumers are questioned regarding this product.
    The table below provides information regarding this sample.

    \begin{array}{c||c|c|c||c|}<br />
& \text{Positive} & \text{Neutral} & \text{Negative} & \text{Total} \\ \hline \hline<br />
\text{Male} & 190 & 70 & 110 & 370 \\ \hline<br />
\text{Female} & 210 & 200 & 130 & 610 \\ \hline\hline\<br />
\text{Total} & 400 & 340 & 240 & 980 \\ \hline \end{array}
    (a) What is the probability that a randomly selected male would have a negative reaction?
    P(\text{neg}\,|\,\text{male}) \;=\;\frac{n(\text{neg} \wedge \text{male})}{n(\text{male})} \;=\;\frac{110}{370} \;=\;\frac{11}{37}


    (b) What is the probability that a randomly selected person would be a female who had a positive reaction?
    P(\text{female}\wedge\text{pos}) \;=\;\frac{n(\text{female}\wedge\text{pos})} {n(\text{Total})} \;=\;\frac{210}{980} \;=\;\frac{3}{14}


    (c) If it is known that a person had a negative reaction to the study,
    what is the probability that the person is male?
    P(\text{male}\,|\,\text{neg}) \;=\;\frac{n(\text{neg}\wedge\text{male})} {n(\text{neg})} \;=\;\frac{110}{240} \;=\;\frac{11}{24}

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