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In a population dataset, I'm trying to calculate the probability that someone has been vaccinated given two known demographic ratios.

For example, if I know that 25% of ALL individuals who are aged 10-19 have received a vaccine, and 60% of ALL individuals who are Hispanic have received a vaccine, what is the probability that a random 15-year-old Hispanic individual has received the vaccine?

It seems like the answer should be fairly simple, but I've gotten totally hardstuck on what the calculation should be. Is there more information needed? I do know a few other ratios about my population: for example, say I know that 70% of the total population has been vaccinated, 28% of the total population is Hispanic, and 11% of the total population is aged 10-19.

I found this question which poses essentially the same problem, but I'm a little confused about whether my data would be considered "independent" or not: Probability of C occurring given both A and B have occurred?. I am only looking to make approximations, so if I need to assume a uniform age distribution across ethnicities, then that is okay.

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Assuming that your events are independent, the probability can be found as follows: $$P(A|B\cap C)=\frac{P(A|B)P(A|C)}{P(A)}$$ $$P(A|B\cap C)=\frac{0.60*0.25}{0.70}$$ which gives us an answer of $\sim 0.21$. These events aren't necessarily independent, however. There might be a trend among young Hispanics to avoid getting vaccinated, even more so than most youth, while older Hispanics get vaccinated similar to other people their age. This would totally change our answer. I don't think it's a stretch to call these things independent, but it's important to keep track of our assumptions.

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