Question

Recent statistics have indicated that of all traffic fatalities from single-vehicle accidents: 45% have passengers of a Sports Utility Vehicle (SUV); 44% were not wearing a seat belt. In addition, of all traffic fatalities involving an SUV, 82% were not wearing a seat belt. A single-vehicle accident produced a fatality. What is the probability that a victim involved in this accident:

(a) was an occupant of an SUV and not wearing a seat belt?

(b) It was determined that the person involved in this accident was wearing a seat beat. What is the probability this person was an occupant of an SUV?

Answer 1

If I understand the conditions of the question correctly, the probability of the vehicle being an SUV is 0.45:

45% have passengers of a Sports Utility Vehicle (SUV)

And the probability that the SUV driver was not wearing a seat belt is 0.82:

of all traffic fatalities involving an SUV, 82% were not wearing a seat belt

P(SUV )=0.45

P(not SUV)=0.55

P(not wearing seat belt)=0.44

P(wearing seat belt)=1-0.44=0.56

P(not suv and wearing seat belt)=0.56-0.45*0.18=0.479

a)P(SUV and not wearing seat belt)=0.45*0.82=0.369

B) P(victim wearing seat belt and an occupant of an SUV) = 0.45*0.18=0.081

Thank you.