In any given year, a male automobile policyholder will make a claim with probability $p_{m}$ and a female policyholder will make a claim with probability $p_{f}$ where $p_{f} \neq p_{m} .$ The fraction of the policyholders that are male is $\alpha, 0<\alpha<1 .$ A policyholder is randomly chosen. If $A_{i}$ denotes the event that this policyholder will make a claim in year $i,$ show that
$$
P\left(A_{2} | A_{1}\right)>P\left(A_{1}\right)
$$
Give an intuitive explanation of why the preceding inequality is true.