The police department is keeping track of distracted drivers and accidents. They have found that if a driver is distracted, the driver has a 30% chance of being in an accident. If the driver is not distracted, the driver has a 2% chance of being in an accident. The probability of a driver being distracted is 10%. If needed, create a tree diagram on a separate piece of paper. Then use the diagram to answer the questions.

a. What is the probability a driver will be in an accident? Explain.
b. What is the probability that a driver who was in an accident was distracted? Explain

Question

The police department is keeping track of distracted drivers and accidents. They have found that if a driver is distracted, the driver has a 30% chance of being in an accident. If the driver is not distracted, the driver has a 2% chance of being in an accident. The probability of a driver being distracted is 10%. If needed, create a tree diagram on a separate piece of paper. Then use the diagram to answer the questions. 

a. What is the probability a driver will be in an accident? Explain. 
b. What is the probability that a driver who was in an accident was distracted? Explain

geneticrockhopper247 · Answer

@phi Sorry for nagging, but can you help with this one, too???

anonymous · Answer

with the tree diagram, i am not sure but this is what i would do
|dw:1363384896370:dw|

phi · Answer

yes, but label the legs with the probability and the "leaves" with the product of the probabilities of each leg.

anonymous · Answer

okay...i get it
thanks!

geneticrockhopper247 · Answer

How would I calculate the probability on this??

phi · Answer

tweak the tree diagram. label the legs with the probability and the "leaves" with the product of the probabilities of each leg.

geneticrockhopper247 · Answer

So the probability a distracted driver will be in an accident is 3% right???

geneticrockhopper247 · Answer

and the probability a non-distracted driver will be in an accident is 1.8%

geneticrockhopper247 · Answer

Added together, 4.8% probability of an accident. Am I right???

geneticrockhopper247 · Answer

@phi ?????

phi · Answer

yes, exactly

geneticrockhopper247 · Answer

okay... Can you check my work on the second part???

geneticrockhopper247 · Answer

Never mind that. Can you walk me through the second part???

phi · Answer

What is the probability that a driver who was in an accident was distracted? Explain

your sample space is restricted to the accident "leaves".   add up those 2 leaves.
the prob of distracted is the prob of being at the distracted leaf divided by the total.

geneticrockhopper247 · Answer

That made no sense to me.

phi · Answer

your tree has 4 leaves.

pick out the two where an accident occurs.

geneticrockhopper247 · Answer

the 2% and the 30%

phi · Answer

you use the probabilities at the leaf. (the #'s used in part a)

geneticrockhopper247 · Answer

.6%???

phi · Answer

something like that, but I got more decimals
what did you get for the total (the denominator)  and for the numerator?

geneticrockhopper247 · Answer

I did .02/.3= .006

phi · Answer

why don't you label the leaves with the numbers you used in part a?

geneticrockhopper247 · Answer

I did cause I re-organized my tree

phi · Answer

please draw it

geneticrockhopper247 · Answer

|dw:1363386712779:dw|
so sorry for the messy drawing