Question

Trucks that travel on highways have to stop at various locations to be weighed and inspected for safe brakes and light systems. Of these​ trucks, 81% are on interstate commerce while 19​% are intrastate. Of the intrastate​ trucks, 3.3​% are flagged for safety defects compared to 0.7​% of those that are on interstate business.

1. Calculate the probability that a randomly chosen truck is an interstate truck and is not flagged for a safety violation.

2. What is the probability that a randomly chosen truck does not have a safety​ defect?

3. If two trucks are chosen​ randomly, determine the probability that only one of the two does not have a safety defect.

Answer 1

1)

P( interstate truck and is not flagged for a safety violation) =P(interstate truck)*P(not flagged|interstate truck) =0.81*(1-0.007)=0.8043

2)

P( does not have a safety​ defect )=P(interstate truck)*P(not flagged|interstate truck)+P( intrastate truck)*P(not flagged| intrastate truck)

=0.81*(1-0.033)+0.19*(1-0.033)=0.9881

3)

P( only one of the two does not have a safety defect) =P(first has and 2nd not)+P(first not and 2nd has) =0.9881*(1-0.9881)+(1-0.9881)*0.9881 =0.0236