The US Safety Administration report on pedestrian injuries i

The US Safety Administration report on pedestrian injuries in traffic accidents found the following statistics: 12% of the cases the victim was under 16 years old, in 22.1% the accident occurred at night, and 5.7% the victim was under 16 and the accident occurred at night. Round answers to the nearest 10th of a percent. What is the probability that the victim was under 16 or the accident occurred at night? What is the probability that the victim was 16 or older and the accident occurred during the day?

Solution

P(Victim was under the age of 16) = 12/100 = 0.12

P(Accident occured at night) = 22.1/100 = 0.221

P(Accident occured at day) = 1 - P(accident occured at night) = 1 - 0.221 = 0.779

P(Accident occured at night and victim was under 16) = 5.7/100 = 0.057

a) Probaibiliy that the victim was under 16 or the accident occured at night

=> P(victim under 16) + P(accident occured at night) - P(victim under 16 and accident occured at night)

=> 0.12 + 0.221 - 0.057

=> 0.284

b) Probaibiliy that the victim was 16 or older and the accident occured at night

=> P(number of victims above 16) * P(accident occured at day) [ since both the events are independent, so they can be multiplied to attain the probability

=> 0.88 * 0.779

=> 0.68552