An insurance company believes that peopl...

An insurance company believes that people can be divided into two classes, those who are accident prone and those who are not. Their statistics show that an accident prone person will not have an accident in a year period with probability 0.4 whereas this probability is 0.2 for the other kind. Given that 30% of people are accident prone, the probability that a new policy holder will have an accident within a year of purchasing a policy is :

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