Question

regina 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
four doctor visits	24%	$100	$1,400
medication	12%	$40	$240

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 $

Explanation:

Step1: Calculate expected cost without insurance

The annual premium is $0$ (probability 100%). For four - doctor visits, the expected cost is $0.24\times1400 = 336$. For medication, the expected cost is $0.12\times240=28.8$. The total expected cost without insurance is $0 + 336+28.8$.

Step2: Calculate sum for no - insurance

$0+336 + 28.8=364.8$

Step3: Calculate expected cost with insurance

The annual premium is $1580$ (probability 100%). For four - doctor visits, the expected cost is $0.24\times100 = 24$. For medication, the expected cost is $0.12\times40 = 4.8$. The total expected cost with insurance is $1580+24 + 4.8$.

Step4: Calculate sum for insurance

$1580+24+4.8 = 1608.8$

Answer:

The expected value of health care without insurance is $\$364.8$
The expected value of health care with insurance is $\$1608.8$