Head.o data are from Mortality Reduction with Air Bag and Seat belt Use in Head-

Question

Head.o data are from Mortality Reduction with Air Bag and Seat belt Use in Head-On Passenger car Collisions Driver Killed 3655 4402 Driver Not Killed 7005 3040 Seat Belt Used Seat Belt Not Used a. If one driver is randomly selected, find the probability he or she was not using a seat belt? b. If one of the drivers is randomly selected, find the probability of getting a driver who used a seat belt or was killed. c. If two drivers are randomly selected with replacement, find the probability that they both used seat belts. d. If three drivers are randomly selected without replacement, find the probability that none of them were killed If A represents the event of randomly selecting one driver included in the table and getting someone who was using a seat belt, what does A represent? Find the value of PlA) e. 13. Three unbiased coins are tossed. What is the probability of getting at most two heads? Construct the sample space and then show your work S points)

Explanation / Answer

a)

P(no seat belt)

= (4402+3040)/(3655+7005+4402+3040)

= 7442/18102

= 0.4111

b)

P(seat belt or killed)

= P(seat belt) + P(killed) - P(seat belt and killed)

= {(3655+7005) + (3655+4402) - 3665}/18102

= 0.8321

c)

P(two drivers used seat belts with replacement)

= (3655+7005)/18102*(3655+7005)/18102

= 0.3474

d) P(three drivers killed without replacement)

= (3655+4402)/18102 *

(3655+4402-1)/18101*

(3655+4400)/18100

= 0.0882

e)

A represent driver wearing seat belt

P(A) = (3665+7005)/18102

= 0.5894

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