5. A 2011 study by The National Safety Council estimated that there are nearly 5

Question

5. A 2011 study by The National Safety Council estimated that there are nearly 5.7 million traffic accidents year. At least 28% of them involved distracted drivers using cell phones or texting. The data showed that 11% of drivers at any time are using cell phones . Car insurance companies base their policy rates on accident data that 2/3/2017 shows drivers have collisions approximately once every 19 years. That’s a 5.26% chance per year. Step D: Given that the driver has an accident, what is the probability that the driver was distracted by a cell phone? Write this event with the correct conditional notation. (1 point) Step E: What is the probability that a randomly selected driver will be distracted by using a cell phone and have an accident? (2 points)

Explanation / Answer

Let, P(DC) denote the probability that the driver was using cell phone whilst driving. P(DC)=0.11.

Let, P(TA) denote the probability that the driver met with an accident. P(TA)=0.0526.

D)

P(DC|TA)=0.28

E)

P(DCTA)=P(DC|TA)*P(TA)=0.28*0.0526=0.014728

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