According to data collected by the Department of Highway Safety and Motor Vehicl

Question

According to data collected by the Department of Highway Safety and Motor Vehicles in Florida on people involved in traffic accidents in 1998, 0.37% suffered a fatal accident, 28.4% did not wear a seat belt, and 0.28% did not wear a seat belt and suffered a fatal accident. What is the probability that an accident involved a person not wearing a seat belt, given that it was a fatal accident? What is the probability that an accident involved a fatal injury, given that the person was not wearing a seat belt? What is the probability that an accident involved a fatal injury, given that the person was wearing a seat belt? How does this compare to (b)?

Explanation / Answer

Probability of fatal accident P(F) = 0.0037

Probability of not wearing seat belt P(S) = 0.284 , P( S') = 0.716

P(F and S) = 0.0028

A)

P(S|F) = P(S and F) / P(F)

= 0.0028 / 0.0037

= 0.756

b)

P(F|S) = P(S and F) / P(S)

= 0.0028 / 0.284

= 0.0098

c)

P( F and S') = 0.0037 - 0.0028 = 0.0009

P(F|S') = P( F and S') / P(S')

= 0.0009 / 0.716

= 0.00125

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