Question

A study showed that 64.7​% of occupants involved in a fatal car crash wore seat belts. Of those in a fatal car crash who wore seat​ belts, 2​% were ejected from the vehicle. For those not wearing seat​ belts, 36% were ejected from the vehicle. Complete parts​ (a) and​ (b) below.

(a) Find the probability that a randomly selected person in a fatal car crash who was ejected from the vehicle was wearing a seatbelt.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

(b) Find the probability that a randomly selected person in a fatal car crash who was not ejected from the vehicle was not wearing a seatbelt.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

Answer 1

Let 'S' be the event of getting a person involved in a fatal car crash wore seat belts

P(S) = 0.647

Let 'S-' be the event of getting a person involved in a fatal car crash not wore seat belts

P(S-) = 1-P(S) = 1-0.647 = 0.353

Let 'E' be the event of getting a person ejected from the vehicle

P(E|S) = 0.02

P(E|S-) = 0.36

a)

The probability that a randomly selected person in a fatal car crash who was ejected from the vehicle was wearing a seat belt is

P(S|E) = ( P(E|S)P(S) ) / { P(E|S)P(S) + P(E|S-)P(S-) }

= (0.02*0.647) / ( 0.02*0.647 + 0.36*0.353 )

= 0.0924

b)

The probability that a randomly selected person in a fatal car crash who was not ejected from the vehicle was not wearing a seat belt.

P(S-|E) = ( P(E|S-)P(S-) ) / { P(E|S)P(S) + P(E|S-)P(S-) }

= (0.36*0.353) / ( 0.02*0.647 + 0.36*0.353 )

= 0.9076