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Math Help - 2 Q. needs 2 ANS.

  1. #1
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    2 Q. needs 2 ANS.

    22. in a city ,25% of the cars emit pollutions to the air of the city .if a car failed to pass the emission of air pollutants with probability 0.99 and if a car that is not emitting air pollutants also fails the test with probability 0.17 .what is the probability that a car that fails the test actually emits air pollution ?

    23.the number of employees working in factories A,B and C are , respectively 50,75 and 100 . suppose that of those employees ,50% ,60 % and 70%,respectively ,are women .assuming that the probability of resignation is the same for men and women and that woman resigned ,what is the probability that she is from factory c ?
    Last edited by compufatwa; November 5th 2007 at 12:32 PM.
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  2. #2
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    Hello, compufatwa!

    I'll do the second one . . .

    These are Conditional Probability problems.
    You're expected to be familiar with the formula: . P(A|B) \:=\:\frac{P(A \wedge B)}{P(B)}


    23. The number of employees at factories A,B and C are , respectively 50, 75 and 100.
    Suppose that of those employees, 50%, 60% and 70%, respectively, are women.

    Assuming that the probability of resignation is the same for men and women
    and that woman resigned, what is the probability that she is from factory C?
    I tabulated the data . . .

    \begin{array}{cccccccc}<br />
& |& \text{Women} &|& \text{Men} &|& \text{Total} & | \\ \hline<br />
A &|& 25 &|& 25 &|&50 &| \\<br />
B &|& 45 &|& 30 &|&75 &| \\<br />
C &|& 70 &|& 30 &|& 100 &| \\ \hline<br />
\text{Total} &|& 140 &|& 85 &|& 225 &| \end{array}


    Formula: . P(\text{from C }|\text{ Woman}) \;=\;\frac{P(\text{from C }\wedge\text{ Woman})}{P(\text{Woman})}


    From the chart, we have: . \begin{Bmatrix}P(\text{from C }\wedge\text{ Woman}) &=& \frac{70}{225} \\<br />
P(\text{Woman}) & = & \frac{140}{225} \end{Bmatrix}


    Therefore: . P(\text{from C }|\text{ Woman}) \;=\;\frac{\frac{70}{225}}{\frac{140}{225}} \;=\;\frac{1}{2}


    But check my reasoning and work . . . please!
    .
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  3. #3
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    Thumbs up

    Soroban thanks alot for the answer
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