Question

Previous Problem Problem List Next Problem (1 point) The U.S. National Highway Traffic Safety Administration gathers data concerning the causes of highway crashes where at least one fatality has occurred. From the 1998 annual study, the following probabilities were determined (BAC is blood-alcohol level): P(BAC =0|Crash with fatality) = 0.613 P(BAC is between .01 and .09|Crash with fatality) = 0.335 P(BAC is greater than .09|Crash with fatality) = 0.054 Suppose over a certain stretch of highway during a 1-year period, the probability of being involved in a crash that results in at least one fatality is 0.027. It has been estimated that 15% of all drivers drive while their BAC is grater than 09. Determine the probability of a crash with at least one fatality if a driver drives while legally intoxicated (BAC greater than 0.09) Probability = Preview My Answers Submit Answers You have attempted this problem 0 times You have unlimited attempts remaining Email Professor Lu We Work Page generated at 10/07/2019 at 08 11am EDT 1996-2017 theme math 4 ww_version We Work 2 13 i sverion PO-2.13 The We Work Project co search Ria

Answer 1

We are given here that:
P( BAC = 0 | crash with fatality ) = 0.613
P( 0.01 < BAC < 0.09 | crash with fatality) = 0.335
P( BAC > 0.09 | crash with fatality ) = 0.054

P( crash with fatality ) = 0.027

P( BAC > 0.09) = 0.15

Using Bayes theorem, we have here:
P( BAC > 0.09 | crash with fatality )P( crash with fatality ) = P( crash with fatality | BAC > 0.09)P(BAC > 0.09)

Putting all the above values, we get here:
0.054*0.027 = P( crash with fatality | BAC > 0.09)*0.15
P( crash with fatality | BAC > 0.09) = 0.054*0.027/ 0.15 = 0.00972

Therefore 0.00972 is the required probability here.