Complete question :
The American Automobile Association (AAA) reports that of car accidents, 56% are caused by aggressive driving. If 3 accidents are chosen at random, find the probability for the following. Please round the final answers to 2 or 3 decimal places.
None are caused by aggressive driving.
At least 1 is caused by aggressve driving
Answer:
P(none caused by aggressive driving ) = 0.085184
P(atleast one caused by aggressive drive) = 0.914816
Explanation:
Given:
Percentage accidents caused by aggressive driving = 56%
Hence,
Probability that an accident is caused by aggressive driving : p(aggressive) = 0.56
p(not aggressive) = 1 - p(aggressive)
p(not aggressive) = 1 - 0.56 = 0.44
A.) If 3 accidents are chosen at random ; probability that none is caused by aggressive driving :
Independent probability :
1st accident * 2nd accident * 3rd accident
P(not aggressive) * p(not aggressive) * p(not aggressive)
0.44 * 0.44 * 0.44 = 0.085184
B.) probability that atleast one is caused by aggressive driving :
Probability that atleast 1 is caused by aggressive driving = (1 - probability that none is caused by aggressive driving)
= 1 - 0.085184 = 0.914816