Does the probability of death increase when there are more people?


Say there is a 1 in 10 chance of death from a virus. My partner suggested that between the two of us, we would have a higher chance of one of us dying. I don’t agree and think that it is still a 1 in 10 chance. But I’m a bit thick when it comes to math…

In: 0

If you treat it as a math problem, then the chances of “death from virus” is fixed because most math problems are assumed to be very simplistic, ideal situations.

Realistically, two people means more interaction with people outside who could be sick (work, shopping, travel), which means higher chances that one of you gets it, which means higher chances that one of you dies from it.

But if there are two people and each person has a 1 in 10 chance of dying. Does that mean together they have a 2 in 10 chance of dying?

The standard way to solve this (assuming your chances are independent which is probably not a real assumption) is to reverse it and calculate the probability of you both living. That would be .9 * .9 = .81. Then, the chance of at least one dying is 1 – .81 = .19. This is less then 2/10.

Assuming that the 10% chance of death was studied from a larger group of people and that is an accurate number then you still have a 10% chance at death.

This is all assuming no outside factors that actually go into deciding your chances of death. For example, if someone is 85 years old with asthma then they’re chances of dying from Covid are higher than a healthy 25 year old with no underlying conditions.

So assuming this virus has a 10% chance of death no matter the other factors then you are correct, the group size doesn’t matter. Every individual person has a 10% chance at death which means 10/100 people will die and 100/1,000 people will die when infected.

Realistically, everyone’s chances of death when infected with a virus is different. I hope this makes sense, lol.

Independent people who don’t live together tend to have independent results from the virus. But that’s not true for people living together.

By living closely with someone, you are increasing the likelihood that one person being exposed leads to more than one person getting exposed, and increasing the average viral load they are exposed to.

So, you are more likely to get infected if they are infected, you are more likely to get reinfected after recovery if they are still infected, and you are more likely to develop severe symptoms or illness with another infected person living in the same place as you.

For more details beyond an ELI5:

Risk from contagious diseases increases at least in proportion with _population density_ when all other things are equal.

So, if we double the number of people per square mile in your area, and change nothing else…. then you have at least doubled the number of times you run into someone in an average day (so doubling your exposure).

If you live in a closed apartment building with 1000 other people, you are much more likely to catch a virus and develop a severe illness from it than someone who lives with 10 other people in the middle of nowhere. All other things being equal.

If the apartment building consists of people who are compulsive about masks and the folks in the middle of nowhere hate masks, you are generally better off in the apartment building, though. Running into someone with a mask has a much lower risk than running into someone without. Like 20-100x lower. This is why rural regions with low population density and low mask usage have just been ravaged by covid at rates very disproportionate to their population density.

It sounds like your partner and yourself are talking about two different things : you’re talking about your individual chance of dying, which would still be 1/10, and they’re talking about the chance that AT LEAST one of you dies (assuming you both catch it), which is higher than 1/10.

Everybody else has already explained the math so I just wanted to point this out.