Drunk Drivers and Traffic Deaths

Date: 05/14/97 at 15:51:12
From: Anonymous
Subject: Another Probability Question

Dr. Math,

Thank you so much for the help with my last question. Here is another 
I am stuck on:
                                1980      1989
Total Traffic Fatalities:      52,600    46,900
Number Involving Alchohol:     28,000    26,100


a) Estimate the probability that a traffic death may be attributed t a
drunken driver. 50 percent

b) If about 2 percent of drivers are legally drunk, about how many 
times more likely is it for a drunken driver to have an accident than 
a sober driver?  

I don't even know where to begin.

Thank you again.

Date: 05/14/97 at 19:22:10
From: Doctor Anthony
Subject: Re: Another Probability Question

We can make up a table as follows:

         | 1980          1989|Totals
     --------------------------------
  Drunk  | 28000       26100 | 54100

  Sober  | 24600       20800 | 45400
    ----------------------------------
  Totals | 52600       46900 | 99500

The probability of an accident being caused by a drunk driver  

     = 54100/99500
     = 0.5437

So we have   

    2 percent cause 54.37 percent of the accidents
   98 percent cause 45.63 percent of the accidents

So drunks are (98/2)(54.37/45.63) times as likely to cause an 
accident

    = 58.38  

So a drunk driver is approximately 58 times as likely to cause an 
accident as a sober driver.   

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/