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LostInParadise's avatar

What do you think of the following method for solving a type of probability problem?

Asked by LostInParadise (31122points) October 21st, 2022
5 responses
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People have a difficult time solving probability problems. I read about a useful way of approaching certain problems. I will first give a problem and then outline the approach to solving it. See if it makes sense.

0.8 percent of the population has a certain disease. The test for the disease is positive for 90% of those who have it. For those who do not have it there is a 7% chance of getting a false positive. If someone tests positive, what is their chance of having the disease?

Here is the approach that I read about – no equations and no algebra. Consider a sample size of 1000 patients. How many of them have the disease? Of those people, how many will test positive? Then find how many of the 1000 do not have the disease, and out of that number, how many will test positive. What is the total number that test positive? Of those, how many actually have the disease? To make things easier, round the numbers involved to the neatest whole number.

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kritiper's avatar

My approach is that you never argue with success.

RayaHope's avatar

See I have no idea how to find the answer, but I am curious to know how you do find it. I tried to figure it out and got really lost and I’m sure way off.

LostInParadise's avatar

Here is how to solve the problem. The sample size is 1000. Of those .8% have the disease. 0.008×1000=8 people have the disease. 90% or about 7 test positive.

992 people do not have the disease. .07×992 or about 70 of them test positive.

A total of 77 people test positive, of which 7 have the disease, so the chances of a person with a positive test result having the disease is 7/77 or about 9 percent.

RayaHope's avatar

^ Thank you, I was way off.

Zaku's avatar

That’s a good technique. I like that it makes the problem concrete (in terms of actual people) rather than remaining with percentage numbers. It’s a great sort of way to reality-check problems, make them more relatable, etc.

That sort of thing tends to be a good way to reality-check math results for story problems, too.

(Rather than rounding, I’d recommend increasing the population amount you’re considering. Multiply by 10, then another 10, etc, until you get the precision you want.)

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