Question

In a recent News, it was reported that light trucks, which include SUV’s , pick-up trucks and minivans, accounted for 40% of all personal vehicles on the road in 2012. Assume the rest are cars. Of every 100,000 cars accidents, 20 involve a fatality; of every 100,000 light trucks accidents, 25 involve a fatality. If a fatal accident is chosen at random, what is the probability the accident involved a light truck?​

Answer 1

• 45.45%

Explanation:

• Light tracks = 40% = 0.4
• Cars = 60% = 0.6

Fatal accidents involving light tracks:

• 25/100000 = 0.00025

Fatal accidents involving cars:

• 20/100000 = 0.0002

Probability of a fatal accident involving a light track:

• p = involving light tracks /involving both cars and light tracks
• p = 0.4*0.00025/(0.4*0.00025 + 0.6*0.0002) = 0.4545
• p = 45.45%