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Thread: am I right?

  1. #1
    Actuary.com - Level II Poster
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    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. #2
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    Quote Originally Posted by pitwen View Post
    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. #3
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    Quote Originally Posted by pitwen View Post
    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%
    Last edited by R_T; December 27th 2009 at 11:12 PM.

  4. #4
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    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?
    Last edited by pitwen; December 28th 2009 at 12:30 AM.

  5. #5
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    Quote Originally Posted by pitwen View Post
    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. #6
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    Quote Originally Posted by pitwen View Post
    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.
    Last edited by R_T; December 28th 2009 at 10:50 AM.

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