SOLUTION: The American Automobile Association (AAA) reports that of the fatal car and truck accidents, 54% are caused by a car driver error. If 3 accidents are chosen at random, find the pro

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Question 266114: The American Automobile Association (AAA) reports that of the fatal car and truck accidents, 54% are caused by a car driver error. If 3 accidents are chosen at random, find the probability that:
a. All are caused by car driver error
b. None are caused by car driver error
c. At least 1 is caused by car driver error
Thanks!

Answer by roseo(33) (Show Source):
You can put this solution on YOUR website!
a. Because each accident is an independent event then the probability of 3 accidents being caused by driver error is .54(.54)(.54)=.157464
b. Because the probability of an accident is not caused by driver error would be 1-.54 or.46. Therefore the probability of 3 accidents not caused by driver error would be (.46)(.46)(.46) =.097336
c.When ever you have a probability question that says at least one then it is asking for the probility of the converse or 1-P(the opposite of the event) so you would need 1-P(that all three accidents were not caused by driver error) or 1-.097336 =.902664