what is the odds to catch the virus

Let's see the 7-day average rate to test positive is $$4\%$$, and I'll be in school for one month. What's the possibility I'll catch a virus this month? $$1-0.96^{30}=0.7$$, so the possibility is $$70\%$$ I will catch the virus in one month. This result cannot be right, what's wrong with my model? Thanks.

• If you assume that there's 4% to catch a virus in one day, then your number is right. It's a power of compounding! If the propensity was so high, I'd skip the activity. – Aksakal Apr 22 at 14:08
• @Aksakal Would you believe the events to be independent? // There's a "related" question on the right that gives me an idea for an analogy. Say I want to go to one of the top 30 colleges in the world, each of which has a 4% admission rate. I apply to all, so my chance of getting in is $1-0.96^{30} = 70\%$. I don't believe that number. – Dave Apr 22 at 14:12
• @Dave, assumption of independence is implicit here. If OP didnt think the hazard rate is independent then the hazard rate itself is obviously not enough to make conclusions. – Aksakal Apr 22 at 14:39
• independence assumption is actually quite common in epidemiology models, e.g. take a look at SIR. the problem in these calculations is truly not the independence, but conditionality. you need to personalize the probability to your situation, e.g. risk factors such as health (diabetes etc.) and behavior. – Aksakal Apr 22 at 14:45
• @Dave, schools are probably independent in their decisions, they don't collude. they use common factors, of course, but that's conditional part. think of probability as $y_i=X_i\beta+\varepsilon_i$, then independence is about $\varepsilon_i$ not $X_i\beta$, which can be conditional part – Aksakal Apr 22 at 15:19