please answer questions 1 - 4

. - A simplified set of data that approximates current insurance costs for someone with no risk factors: Claim Payout Base Probability of Claim Contribution to Premium $1,000,000 0.00007 $70 $100,000 0.0005 $50 $50,000 0.0008 $40 $10,000 0.008 $80 $5,000 015 $75 $1,000 ,065 $65 Total $380 For a person with no risk factors, their 6-month premium would be the sum of the right column plus the average overhead cost or $380 + $100 = $480. That's $80 per month Risk factors affect the probability of specific claim amounts. These become complicated for people with more than one risk factor, so we will only look at people with one risk factor (for multiple risk factors, you would multiply the base probability by ALL the listed values that apply). 18-25: multiply base probability x 3 for all claim amounts Age 26-69: no change 70 +: base x 2 for $10k, $50k, $100k claims Female: no change Gender Male : base x 1.15 for $50k, 5100k, and $1M claims Single: no change Marital Status Married: base x 0.9 for $50k, $100K, SIM claims No tickets or accidents: no change History (past 7 years) For each ticket: base x 1.1 for $50, $100k, and SIM claims For each accident: base x 1.3 for $50k, $100k, and $1M claims Rural: base x 0.8 for $1,$sk, and $10k claims Location Suburban: no change Urban: base x 1.2 for Sik, $5k, and $10k claims 0-10 miles: no change Commute 10-30 miles: base x 1.1 for $SOK, $100k, and $1M claims 30+ miles: base x 13 for $SOK, $100k, and SIM claims Example: A person whose only risk factor was a 40 mile commute would need to modify their probabilities for the $50k, $100k, and $1M claims as shown: . . . Claim Payout $1,000,000 $100,000 $50,000 $10,000 55,000 $1,000 Base Probability of Claim 0.00007 * 1.3=0.000091 0.0005 1.3 -0.00065 0.0008 * 1.3 0.00104 0.008 .015 .065 Contribution to Premium $91 $65 $52 $80 $75 $65 . = Hence their 6-month premium would be $428 + $100 - $528 Sopha is 21, female, single, with no tickets or accidents, and lives in a suburban area 8 miles from her college. Thus her only risk factor is her age. 1. What is the probability she will get in a car accident requiring the insurance company to pay a $1,000,000 claim during this six-month premium period? 2. Fill in the rest of the probability column the same way you found the probability of the $1,000,000 claim, and then multiply across the rows. Claim Payout Probability of Claim Contribution to Premium $1,000,000 . - $100,000 $50,000 $10,000 . 11 $5,000 11 $1,000 = 3. What is the expected value that the insurance company will have to pay in claims for someone with Sopha's risk factors every six months? 4. What is Sopha's six month premium