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1. ## am I right?

Problem 9.13
A study of drinking and driving has found that 40% of all fatal auto accidents
are attributed to drunk drivers, 1% of all auto accidents are fatal, and drunk
drivers are responsible for 20% of all accidents
. Find the percentage of nonfatal
accidents caused by drivers who are not drunk.

The answer was 80.2%, cannot be right? As, drunkards have contributed 20% of all accidents, accidents caused by non drunkards should be 80%, therefore nonfatal accidents caused by non drunkards should be at most 80%? am I correct?

2. Originally Posted by pitwen
Problem 9.13
A study of drinking and driving has found that 40% of all fatal auto accidents
are attributed to drunk drivers, 1% of all auto accidents are fatal, and drunk
drivers are responsible for 20% of all accidents
. Find the percentage of nonfatal
accidents caused by drivers who are not drunk.

The answer was 80.2%, cannot be right? As, drunkards have contributed 20% of all accidents, accidents caused by non drunkards should be 80%, therefore nonfatal accidents caused by non drunkards should be at most 80%? am I correct?
Let DD be Drunk Drivers, NDD be Non-Drunk Drivers.
Let F be Fatal, NF be Non Fatal.

F = .01 => NF = .99
(F & DD) / F = .40 => F & DD = .004

DD = .2
Since F & DD = .004 and DD alone = .2, NF && DD = .196
Since NF alone = .99 and NF & DD = .196, NF & NDD = .794

The question wants the percentage of NF's caused by NDD:
(NF & NDD)/ (NF) = .794/.99 = .802020202...

3. Originally Posted by pitwen
Problem 9.13
A study of drinking and driving has found that 40% of all fatal auto accidents
are attributed to drunk drivers, 1% of all auto accidents are fatal, and drunk
drivers are responsible for 20% of all accidents
. Find the percentage of nonfatal
accidents caused by drivers who are not drunk.

The answer was 80.2%, cannot be right? As, drunkards have contributed 20% of all accidents, accidents caused by non drunkards should be 80%, therefore nonfatal accidents caused by non drunkards should be at most 80%? am I correct?
Actually, I think Kenneth is right. Here is another way to look at it. 1000 people were involved in accidents 10 were fatalities, 6 of them attributed
to to nondrunk drivers. A total 0f 800 -6 = 794 people were involved in nonfatal accidents by drivers who weren't drunk and there are 990 nonfatalities
794/990 =80.2%

4. but how come this should be a conditional probability, ie conditional on nonfatalities? but not 79.4%, the probability that the person is not drunk and nonfatality?

5. Originally Posted by pitwen
but how come this should be a conditional probability, ie conditional on nonfatalities? but not 79.4%, the probability that the person is not drunk and nonfatality?
The question asks: "Find the percentage of nonfatal accidents caused by drivers who are not drunk."

So, we are ONLY looking at nonfatal accidents. We aren't looking at fatal accidents, alien abductions or sweet 16 birthday parties. So, of those nonfatal accidents, which ones were caused by non-drunk drivers?

6. Originally Posted by pitwen
but how come this should be a conditional probability, ie conditional on nonfatalities? but not 79.4%, the probability that the person is not drunk and nonfatality?
You are essentially being asked to compute the conditonal probability that person was not a drunk driver given that the accident was not fatal.