# Thread: Conditional Prob (I believe)

1. ## 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?

2. Hi dw, draw yourself a Karnaugh Map. You'll find $0.39 \times 0.28 = 0.1092$

3. Originally Posted by pickslides
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?

4. Originally Posted by dwsmith
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 ....

5. Pickslides,

I really want to know how to use a Karnaugh Map in these cases.

6. dw, here is the format, assuming independence $\displaystyle \implies P(A \cap B) = P(A)\times P(B)$

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

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