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Math Help - Conditional Prob (I believe)

  1. #1
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    Conditional Prob (I believe)

    28% of drivers involved in a fatal car crashes were between 20-29

    39% of drivers in a fatal car accident had a blood alcohol of at least 0.01

    In what % of fatal crashes were the drivers between 20-29 and found to have a blood alcohol level greater than 0.01?

    \displaystyle P(\text{20-29}|>0.01)=\frac{P(\text{20-29} \ \cap \ >0.01)}{P(>0.01)}=\frac{.28}{.39}\approx .7179

    However, the solution is .1092. How did the book get this answer?
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    Hi dw, draw yourself a Karnaugh Map. You'll find 0.39 \times 0.28 = 0.1092
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    Quote Originally Posted by pickslides View Post
    Hi dw, draw yourself a Karnaugh Map. You'll find 0.39 \times 0.28 = 0.1092
    I know how to make one for circuits but how do I apply it to Probabilities?
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    Quote Originally Posted by dwsmith View Post
    28% of drivers involved in a fatal car crashes were between 20-29

    39% of drivers in a fatal car accident had a blood alcohol of at least 0.01

    In what % of fatal crashes were the drivers between 20-29 and found to have a blood alcohol level greater than 0.01?

    \displaystyle P(\text{20-29}|>0.01)=\frac{P(\text{20-29} \ \cap \ >0.01)}{P(>0.01)}=\frac{.28}{.39}\approx .7179

    However, the solution is .1092. How did the book get this answer?
    P(\text{20-29} \, \cap >0.01) \neq 0.28. In fact, P(\text{20-29})  = 0.28. Big difference between these two probabilities and obviously there's not enough information to calculate a conditional probability.

    In fact, the question requires you to calculate P(\text{20-29} \cap >0.01). The book's answer has been calculated assuming independence of these two events ....
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    Pickslides,

    I really want to know how to use a Karnaugh Map in these cases.
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    dw, here is the format, assuming independence \displaystyle \implies P(A \cap B) = P(A)\times P(B)

    \displaystyle \begin{array}{|c|c|c|c|}<br />
\ \dots & \geq 0.01 & <0.01 & \dots  \\ \hline<br />
20-90 & P(20-29~ \cap \geq 0.01)& P(20-29~ \cap < 0.01)& P(20-29) \\ (20-29)' & P((20-29)' \cap \geq 0.01)& P((20-29)' \cap < 0.01) & P(20-29)' \\ \hline<br />
 \dots & P(\geq 0.01)& P(<0.01)& \dots \\ \hline \end{array}

    This isn't my finest Latex effort (Soroban, help me!)
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