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There is a 1 percent chance that you will have healthcare bills of $100,000, a 19 percent chance that you will have healthcar
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a)

Out of pocket exepenses in case of medical bills of $100000=$5000

Out of pocket exepenses in case of medical bills of $10000=$5000

Out of pocket exepenses in case of medical bills of $500=$500

Expected out of pocket expenses=1%*5000+19%*5000+60%*500=$1300

Insurance benefit in case of medical bills of $100000=100000-5000=$95000

Insurance benefit in case of medical bills of $10000=10000-5000=$5000

Insurance benefit in case of medical bills of $500=$0

Expected Insurance benefit=1%*95000+19%*5000+60%*0=$1900

Annual premium=1900*116%=$2204

Total expected expense in case of a insurance policy with $5000 deductible =1300+2204=$3504

Let us consider the case with full coverage

Insurance benefit in case of medical bills of $100000=$100000

Insurance benefit in case of medical bills of $10000=10000

Insurance benefit in case of medical bills of $500=500

Expected Insurance benefit=1%*100000+19%*10000+60%*500=$3200

Annual premium=3200*116%=$3712

Total expected expense in case of a insurance policy with full coverage =0+$3712=$3712

We can see that expected expense is more in case of full coverage. I will go for $5000 deductible policy

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