Hello. I know it's must be simple. But I want to ask.

[ldontKnow]

Hello,

Thera are 33.7% vaccinated people in the country, but in hospitals, only 6% of vaccinated people. What percentage of vaccinated people would be in hospitals, if 50% people were vaccinated in the country? Is that just the answer of (50*6)/33.7?

 

[JeffM]

There is no way to answer this without knowing what you have studied in math.

If I remember from a long time ago, epidemiologists use Markov processes. Is that what you are studying? We probably have someone who can guide you through those (but I have forgotten).

Is this a problem in Bayesian probability? We have many who can guide you through

Or is this a question from beginning algebra?

In our guidelines. we ask you to tell us what you are studying so we have at least a clue what kind of math you know.

Now think about your answer with plain common sense. What do you expect to happen to the number hospitalized if the number vaccinated goes up? Therefore what do expect to happen to the ratio of vaccinated in hospital over the total in hospital?

Does your answer meet the test of common sense?

 

[Otis]

… is … the answer … (50*6)/33.7

Hi IDK. That's the answer I got. But, I've assumed that the ratio (hospital vaccinated)/(country vaccinated) remains constant. In that case, the proportion is:

[math]\frac{6}{33.7} = \frac{?}{50}[/math]
To find the unknown number, I multiplied on the diagonal and then divided by the number not used.

?

 

[Dr.Peterson]

Hello,

There are 33.7% vaccinated people in the country, but in hospitals, only 6% of vaccinated people. What percentage of vaccinated people would be in hospitals, if 50% people were vaccinated in the country? Is that just the answer of (50*6)/33.7?

I want to be sure what the question means, as the grammar is unclear. It's easy to misstate, or misread, percentages.

As I read it, 33.7% of the people in the country are vaccinated, but only 6% of the people in hospitals are vaccinated, presumably because unvaccinated people are more likely to be in the hospital (for several possible reasons).

[I don't think you mean that 33.7% of vaccinated people live in the country, and 6% of them are in the hospital!]

Then you are asked, if 50% of the people in the country were vaccinated (but some other unstated conditions remain unchanged), what percent of the people in the hospital would be vaccinated. [Not, what percent of all vaccinated people would be in hospitals.]

Is that correct? If there is anything in the context of the problem (such as the ideas JeffM asked about, or something else in the specific topics you are learning) that might clarify the meaning, and particularly what is to be assumed constant, that will help.

If this were from a probability course, I would be thinking in terms of Bayes theorem. In an algebra class, you might be expected to assume proportionality, but there is no good reason to do so. (Too many texts at that level don't teach the importance of determining that.)

 

[ldontKnow]

There is no way to answer this without knowing what you have studied in math.

If I remember from a long time ago, epidemiologists use Markov processes. Is that what you are studying? We probably have someone who can guide you through those (but I have forgotten).

Is this a problem in Bayesian probability? We have many who can guide you through

Or is this a question from beginning algebra?

In our guidelines. we ask you to tell us what you are studying so we have at least a clue what kind of math you know.

Now think about your answer with plain common sense. What do you expect to happen to the number hospitalized if the number vaccinated goes up? Therefore what do expect to happen to the ratio of vaccinated in hospital over the total in hospital?

Does your answer meet the test of common sense?

This a question from beginning algebra. Unstated conditions remain unchanged. I'm not studying medicine. In common sense, I know, that if more people were vaccinated, more of them will get to hospital, because some people get sick badly, even if they are vaccinated. I was just thinking, that is probability to get to the hospital if you are vaccinated and what is probability to get to hospital, if you are not vaccinated. So I thought, that at first people vaccinated and not outside hospitals, must be 50/50. And then according to that, adjust 6/94 ratio in hospitals.

 

[ldontKnow]

Hi IDK. That's the answer I got. But, I've assumed that the ratio (hospital vaccinated)/(country vaccinated) remains constant. In that case, the proportion is:

[math]\frac{6}{33.7} = \frac{?}{50}[/math]
To find the unknown number, I multiplied on the diagonal and then divided by the number not used.

?

Yes. Maybe it's just that simple. I just wanted confirmation.

 

[ldontKnow]

I want to be sure what the question means, as the grammar is unclear. It's easy to misstate, or misread, percentages.

As I read it, 33.7% of the people in the country are vaccinated, but only 6% of the people in hospitals are vaccinated, presumably because unvaccinated people are more likely to be in the hospital (for several possible reasons).

[I don't think you mean that 33.7% of vaccinated people live in the country, and 6% of them are in the hospital!]

Then you are asked, if 50% of the people in the country were vaccinated (but some other unstated conditions remain unchanged), what percent of the people in the hospital would be vaccinated. [Not, what percent of all vaccinated people would be in hospitals.]

Is that correct? If there is anything in the context of the problem (such as the ideas JeffM asked about, or something else in the specific topics you are learning) that might clarify the meaning, and particularly what is to be assumed constant, that will help.

If this were from a probability course, I would be thinking in terms of Bayes theorem. In an algebra class, you might be expected to assume proportionality, but there is no good reason to do so. (Too many texts at that level don't teach the importance of determining that.)

Sorry, for the unclear grammar. Outside hospitals, in all the state, 33.7% of all people are vaccinated. People with COVID case in hospitals are only 6% vaccinated. What is the probability to get to hospital, if I'm vaccinated and that probability, if I'm not vaccinated. Unstated conditions remain unchanged.

 

[JeffM]

Sorry, for the unclear grammar. Outside hospitals, in all the state, 33.7% of all people are vaccinated. People with COVID case in hospitals are only 6% vaccinated. What is the probability to get to hospital, if I'm vaccinated and that probability, if I'm not vaccinated. Unstated conditions remain unchanged.

Three different questions.

If 6% of those currently hospitalized with COVID were previously inoculated, that is good evidence that inoculation reduces your probability of getting seriously ill if you are later infected to no more than 6%. It is not a mathematical proof, but it is very strong evidence. The percentage of the population that is inoculated is irrelevant to that question.

That 6% statistic does not indicate what the probability of getting infected after inoculation may be. Do you see the difference? By the way, the wife of a good friend of mine got COVID after both inoculations; she is miserable but in no need of a hospital. The percentage of those hospitalized after inoculation places a lower bound on the probability of infection after inoculation. The true number is more than 6%, but we do not know how much more.

Moreover, that 6% statistic says absolutely nothing about the probability of getting infected with COVID if a higher percentage of the population were inoculated.

 

[Dr.Peterson]

Sorry, for the unclear grammar. Outside hospitals, in all the state, 33.7% of all people are vaccinated. People with COVID case in hospitals are only 6% vaccinated. What is the probability to get to hospital, if I'm vaccinated and that probability, if I'm not vaccinated. Unstated conditions remain unchanged.

I think you're saying, not that this is a problem from an algebra course, but that it's a real-life question of your own that you think needs only simple algebra.

There isn't enough information here to answer your question.

But I searched for examples of related calculations that do have enough information, and found one page that is interesting:

Conditional probabilities and imperfect vaccines

Why is it plausible most future Covid-19 hospitalisations are among those vaccinated?

anthonybmasters.medium.com

Your question is similar to standard questions about accuracy of testing. Here is an example of that, showing the sort of data you need:

COVID-19, Bayes’ theorem and taking probabilistic decisions.

No test for is 100% accurate to detect the novel coronavirus! However, we feel satisfied when we are told that the tests are 98.5%…

towardsdatascience.com

Replace "tests positive" with "is vaccinated" to see the parallel.

 

[Deleted member 4993]

Hello,

Thera are 33.7% vaccinated people in the country, but in hospitals, only 6% of vaccinated people. What percentage of vaccinated people would be in hospitals, if 50% people were vaccinated in the country? Is that just the answer of (50*6)/33.7?

Suppose restate the question in the following way:

Thera are 33.7% COVID_vaccinated people in the country, but in hospitals, only 6% of COVID_vaccinated people (- for complications with COVID). What percentage of vaccinated people would be in hospitals - for complications with COVID,, if 50% people were vaccinated in the country?

As of yet, that question is still being investigated. Hope is that would be ~0%.

 

[ldontKnow]

Suppose restate the question in the following way:

Thera are 33.7% COVID_vaccinated people in the country, but in hospitals, only 6% of COVID_vaccinated people (- for complications with COVID). What percentage of vaccinated people would be in hospitals - for complications with COVID,, if 50% people were vaccinated in the country?

As of yet, that question is still being investigated. Hope is that would be ~0%.

Yes, you restructured my question very well.

 

[Otis]

This a question from beginning algebra.

That's what I'd assumed because I couldn't answer it any other way. Word problems at that level don't always comport with reality. Many are cooked up just for practicing particular concepts/methods.

?