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Current time:0:00Total duration:9:16

Comparing insurance with expected value

Video transcript

Paul has the option between a high deductible or a low or a low deductible health insurance plan and when we talk about the deductible and health insurance if someone says that they have a plan with a thousand dollar deductible that means that the insurance company only pays a medical costs after the first thousand dollars so if you have a thousand dollar deductible and you say incur medical costs of $800 you're going to pay that $800 the insurance company won't pay anything if your deductible of $1,000 and your total medical costs are twelve hundred you're going to pay the first thousand and then the insurance company will kick in after that so with that out of the way let's think about his two plans if Paul chooses the low deductible plan he will have to pay the first thousand dollars of any let me do that in purple the first thousand dollars of any medical costs the low deductible plan costs eight thousand dollars for a year so in this situation he's gonna pay eight thousand dollars to get the insurance if he has nine hundred dollars of medical expenses the insurance company still pays nothing if he is two thousand dollars of medical expenses then he pays the first thousand and then the insurance company would pay the next thousand if he has ten thousand and medical expenses he would pay the first thousand and then the insurance company would pay the next nine thousand if Paul chooses a high deductible plan he will have to pay the first 2500 of any medical costs the high deductible plan costs 7,500 a year and it makes sense that the high deductible plan costs less than the low deductible plan because here the insurance doesn't kick in until he has over $2,500 of medical expenses while here was only a thousand to help himself choose a plan Paul found some statistics about common health problems for people similar to him assumed at the table below and I put it up here on the right correctly shows the probabilities and costs of total medical incidents within the next year so this right over here it's saying what's the probability is zero in medical cost what's the probability of well he has a 25% probability of $1000 20% probably four thousand dollars and this is a simplification a pretty dramatic simplification from the real world and the real world the way this makes it sound is there's only five possible medical costs that someone might have zero one thousand four thousand seven thousand to fifteen thousand in the real world you could have twenty dollars in medical costs you could have twenty thousand you could have nine hundred ninety nine dollars so in the real world there's many many more situations here that you would have to kind of redistribute the probabilities accordingly but what that said this isn't a bad approximation it's just saying okay you know roughly if that is the if you if you if you wanted to construct this so it's easier to do the math which which the problem writers have done say look okay 30% zero 25% $1000 this is pretty indicative if you had to kind of group all of the possible costs into some major into some major buckets so it's probably at least a pretty good method for figuring out which insurance policy someone should use so this including the cost of insurance what are Paul's expected total medical costs with the low deductible plan round your answer to the nearest cent so actually I'll get the calculator out for this so at the low whoops with the low deductible plan here low deductible plan he's going to have to spend his total cost he's gonna spend eight thousand no matter what eight whoops what happened to my calculator he's gonna spend eight thousand Mike I'm having issues he's gonna spend eight thousand no matter no matter what so that is eight thousand dollars and then let's see there's a 30% probability he has spends nothing I could just write that as plus 0.3 times zero and I will write it just so that you see I'm taking that into account and there's a 25% chance that he has a thousand dollars in medical costs and the low deductible plan he starts to pay that thousand dollars so plus 0.25 percent chance that he pays $1,000 $1,000 and then you might say okay plus 0.2 times 4,000 but remember if if his costs are four if his medical costs are four thousand he's not going to pay that four thousand he's only going to pay the first thousand so it's really plus point to in this situation his out-of-pocket costs are only $1,000 the insurance company will pay will pay the next three thousand so 0.2 times a thousand and then plus plus point to 20% chance even if he has seven thousand in medical costs he's only have to pay he's only going to have to pay the first thousand so 0.2 times a thousand again and then plus 0.05 times once again a thousand if he has 15,000 expenses he's only going to have to pay the first thousand times one thousand and we get eight thousand seven hundred dollars and one way you could have thought about it is okay he's gonna have to pay eight thousand eight thousand dollars no matter what and the all of the situations where he ends up where he ends up paying that's anything that's these four situations right over here there's a 70% probability of falling into one of these four situations and in any one of these he only has to pay a thousand dollars the insurance company pays everything after that so you could say eight thousand plus there's a 70% chance that he's going to pay one thousand and once again this is kind of this tables a it's a pretty big simplification from from the real world there's probably a lot of scenarios where you would have to pay $500 or $600 or whatever it might be but let's just go with this and so that's essentially a simplification there's a 70 percent chance that he's going to have to pay a thousand dollars and so that's a $700 expected cost from that plus the 8,000 from the insurance gets us to eighty seven eighty seven hundred dollars so let's let's write that down so eighty seven eighty seven hundred my pen is really acting up I don't know what's going on here I think I have to get a new tablet maybe you can't even read that let me write this 87 whoops $8,700 including the cost of insurance what our pauls expect total medical costs with the high deductible plan round your answer to the nearest cent so let's look at the high deductible plan so he's gonna pay 7,500 no matter what 7,500 no matter what and then in so there's a zero we could write zero dollars times 30% or 30% times zero dollars but that's just going to be zero there's a 25% chance he spends a thousand dollars so plus 0.25 times 1,000 there's a 20% chance plus 0.2 he's not gonna spend 4000 here he's going to spend the first 2500 so it's a 20% chance he spends 2500 so times 2500 insurance company will pay the next 1500 plus another 20% chance even in this situation he only has to pay 2500 so times 2500 2500 and then finally plus there's a 5% chance even in this situation he only has to pay the first 2500 times 2500 gets us to eight thousand eight hundred and seventy-five dollars so eight thousand eight hundred and seventy-five seventy-five dollars and once again you could think about it as okay there's a 25% chance that he pays a thousand and then there is a forty five percent chance that he pays $2,500 all of these situations he's paying $2,500 but either way you would get eight thousand eight hundred and seventy five if Paul wants the best pay off in the long run and must buy one of the two insurance plans he should purchase the well his expected total cost of medical of cost of insurance including medical costs is lower with the low deductible plan so this one he should go the low low deductible low deductible which once again you know you shouldn't use these videos as kind of insurance advice this is actually but else it's an interesting way to think about it it's typically what not always typically the case at the low deductible plan it's going to have a higher long-term or the low deductible plan it's going to have a is going to be a better deal it's usually the well I won't I want making the actuarial statements but at least in this situation the low deductible plan seems like the better deal he has lower expected total costs given these probabilities