Final answer:
To find the expected value of health care costs with and without insurance, multiply each cost by its probability and sum the results. The expected value for health care without insurance is $4,181.25 and with insurance is $1,917.50.
Step-by-step explanation:
The student's question pertains to calculating the expected value for health care costs with and without insurance using given probabilities and costs. To determine the expected value of health care without insurance, you would multiply each cost by its respective probability and then sum these values:
- Premium: $0 (since this is a cost with insurance only)
- Doctor visits: 5 visits × $1,750 × 45% probability = $3,937.50
- Medication: $325 × 75% probability = $243.75
Adding these gives the expected value for health care without insurance:
$0 + $3,937.50 + $243.75 = $4,181.25
The expected value for health care with insurance similarly combines the insurance plan premium and the reduced costs for doctor visits and medication, also adjusted for probability:
- Premium: $1,580 (100% probability as it's a fixed annual cost)
- Doctor visits: 5 visits × $125 × 45% probability = $281.25
- Medication: $75 × 75% probability = $56.25
The total expected value for health care with insurance is:
$1,580 + $281.25 + $56.25 = $1,917.50