Olivia used her past health history and information about her doctor visits to create this table to compare health costs with and without insurance. Description of service probability of needing the service cost with insurance plan cost without insurance plan annual premium 100% $1,580 $0 three doctor visits 32% $75 $1,050 medication 45% $72 $225 what is the expected value of each option? the expected value of health care without insurance is $. The expected value of health care with insurance is $.
To calculate the expected value of each option, we need to multiply the probability of needing the service by the cost of the service and sum up all the values.
For the option without insurance:
The probability of needing the annual premium service is 100%, so the expected cost for it is: $1,580.
The probability of needing the three doctor visits is 32%, so the expected cost for them is: 0.32 * $1,050 = $336.
The probability of needing the medication is 45%, so the expected cost for it is: 0.45 * $225 = $101.25.
The expected value of health care without insurance is the sum of these costs: $1,580 + $336 + $101.25 = $2,017.25.
For the option with insurance:
The annual premium service cost is $1,580, regardless of the probability of needing it.
The probability of needing the three doctor visits is 32%, so the expected cost for them is: 0.32 * $75 = $24.
The probability of needing the medication is 45%, so the expected cost for it is: 0.45 * $72 = $32.40.
The expected value of health care with insurance is the sum of these costs: $1,580 + $24 + $32.40 = $1,636.40.
Therefore, the expected value of health care without insurance is $2,017.25, and the expected value of health care with insurance is $1,636.40.