Texas HS Advanced Quantitative Reasoning Question of the Day

Let $P=60$, $L=400$; buy because $L-P=340$ is positive.

Let $P=60$, $p=0.25$, $L=400$, $d=50$; insured expected cost is $P+p(L-d)=60+0.25\times 350=147.5$; since $147.5<100$, buy.

Let $P=50$ (deductible), $p=0.25$, $L=400$; uninsured expected cost $pL=100$, insured expected cost $P+pd=50+12.5=62.5$; buy.

Let $P=60$ (premium), $p=0.25$ (probability), $L=400$ (loss), $d=50$ (deductible); uninsured expected cost $pL=0.25\times 400=100$; insured expected cost $P+pd=60+0.25\times 50=72.5$; buy.