Possible error in 377-5

So the screen is 377-5 (I cannot pick the tag as such).
https://app.dataquest.io/m/377/estimating-probabilities/5/the-true-probability-value

I am probably misreading something, but if the random experiment was performed 200 times, then the math should add up:

"An insurance company conducted a study with 200 individuals, and found that:

87 individuals opted for at least a life insurance policy.
40 individuals opted for at least life and car insurance policies.
63 individuals opted for at least a house insurance policy.
160 individuals opted for at least one type of insurance policy."

When I add 87 and 63, I get 150. I believe this should be 160 because the two types of insurances (assumption) is life or house, and that is the value you get when you add up the numbers. This would change the answer to “the probability that an individual opts for no insurance at all” question.

When determining the number who opt out, the answer:
p_no = (200-160)/200

should be:
p_no = (200-150)/200

Otherwise, shouldn’t the numbers all add up to 200? 87 + 40 + 63 + 10 (those who did not buy a policy?)

Much appreciated.

Hi Amaki. I’m a student here so my answer isn’t DQ’s. You’re taking an overly simplistic approach to the numbers. When you see the statement “at least a life insurance” or “at least a car insurance” you cannot simply add up the numbers. This is because “at least” implies that some of those people have only 1 insurance while some others have more than 1. Maybe 2. Maybe 3. If you simply add up the numbers, you’ll make the mistake of overcounting. That is, you’ll end up counting people twice. For instance, Mr. A may be in the group of people who have at least a life insurance(87 people) . If Mr. A also has a house insurance, he’ll automatically be in the group of 63 people. If you add those numbers up you’ll have counted Mr. A twice. We don’t know the exact numbers until we see the entire distribution. In this problem you mention, you’re asked to find the number of people who have no insurance at all. That’s simply the total number of people minus the number of people who have at least one insurance. Good luck