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My response consists of two parts.
(1) First part is to say that the problem is worded / posed / formulated INCORRECTLY.
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Because one client may have more than one car,
and we even don't know, how many cars an average client does have.
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The correct question, instead of (a), should be
a) What is the expected mean annual payment to a client per each one single care ?
(2) If you agree with this re-formulation, then here is the second part of my post,
which is the solution and the answer to this re-formulated question:
Expected mean annual payment to a client per each one single care is
E = 0.02*15000 + 0.05*8000 + 0.1*5000 = 1200 dollars. ANSWER
Solved.