Conditional probability of making claim by automobile insurance policyholder

[Win_odd Dhamnekar]

Is the above intuitive explanation of " why the inequality [imath] P(A_2|A_1) > P(A_1) [/imath] is true" correct?

 

[BigBeachBanana]

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Is the above intuitive explanation of " why the inequality [imath] P(A_2|A_1) > P(A_1) [/imath] is true" correct?

You stated that the inequality is true, but haven't shown any reasoning.
So why is this true, mathematically? [imath]\frac{\alpha(p_m)^2+(1-\alpha)(p_f)^2}{\alpha(p_m)+(1-\alpha)(p_f)}>\alpha(p_m)+(1-\alpha)(p_f)[/imath]

The intuitive reason is if a person has a history of getting making claims, they'll have a tendency to make more claims. That's why insurance companies raise your premium after you filed a claim.

 

[Steven G]

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Your whole job is to show the last line you wrote is true and all you did was just say that it is true! Why is what is on the left hand side of the inequality >P(A!)??????
I would award very small points for this work on an exam.