Data compiled by the Highway Patrol Department regarding the use of seat-belts b
ID: 3251892 • Letter: D
Question
Data compiled by the Highway Patrol Department regarding the use of seat-belts by drivers in a certain area after the passage of a compulsory seat-belt law are shown in the accompanying table. (Round your answers to three decimal places.)
(a) If a driver in that area is stopped for a moving violation, what is the probability that he or she will have a seat-belt on?
(b) If a driver in that area is stopped for a moving violation, what is the probability that he or she will not have a seat-belt on?
Drivers in Group Percent of Group Stopped
for Moving Violation Group I
(using seat-belts) 62 0.3 Group II
(not using seat-belts) 38 0.5
Explanation / Answer
probability that a randomly selected driver uses seat belt
P(S) = 0.62
P(S') = 0.38
probability that a driver is stopped for moving violation and using seat belt
P(v|s) =0.003
probability that a driver is stopped for moving violation and not using seat belt
P(v|s') = 0.005
a)
Required probability = P(s|v)
= P(v|s) *P(s)/P(v|s) *P(s) +P(v|s')*P(s')
= 0.003 * 0.62/(0.003*0.62 + 0.005*0.38)
= 0.4946
b)
Required probability = P(s'|v)
= P(v|s') *P(s')/P(v|s) *P(s) +P(v|s')*P(s')
= 0.005*0.38 / (0.003*0.62 + 0.005*0.38)
= 0.5053
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