An insurance company survey shows that 96% of all Ontario drivers wear seatbelts.

An insurance company survey shows that 96% of all Ontario drivers wear seatbelts. For those who wear a seatbelt, it is estimated that the chance of getting a serious injury in a car accident is 18%. For those who do not wear a seatbelt, the chance of getting a serious injury is 87%.

a) If in a randomly selected car accident the driver was seriously hurt, what is the probability that the driver was not wearing a seatbelt? (Round the answer to 3 decimal places)

b) If in a randomly selected car accident the driver was not seriously hurt, what is the probability that the driver was wearing a seatbelt? (Round the answer to 3 decimal places)

Expert Solution

a)

P(seriously hurt) =P(wore seat belt)*P(seriously hurt| wore seat belt)+P(not wore seat belt)*P(seriously hurt|not wore seat belt)

=0.96*0.18+(1-0.96)*0.87 =0.2076

therefore P(not wore seat belt given seriously hurt)

=P(not wore seat belt)*P(seriously hurt|not wore seat belt)/P(seriously hurt)

=(1-0.96)*0.87/0.2076 =0.168

b)

P(not seriously hurt) =1-P(seriously hurt) =1-0.2076 =0.7924

therefore P( wearing a seatbelt given not seriously hurt )

=P(wore seat belt)*P(not seriously hurt| wore seat belt)/P(not seriously hurt)

=0.96*(1-0.18)/0.7924 =0.993

orchestra answered 2 years ago

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