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.

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

P(none caused by aggressive driving ) = 0.085184

P(atleast one caused by aggressive drive) = 0.914816

Step-by-step 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

the answer is 62

560

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