Conditional Probability vs Normal

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SUMMARY

The discussion centers on calculating conditional probabilities related to disease prevalence using provided data. The user seeks to determine the probability of having the disease among the total population, utilizing the formula P(Having the disease) = (66 + 5) / 776. Participants confirm the approach and clarify that while the probabilities are conditional, the data allows for straightforward calculations without needing to delve into complex conditional probability expressions. The law of total probability is mentioned as a potential method, but deemed unnecessary for this scenario.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with conditional probability
  • Knowledge of the law of total probability
  • Ability to interpret statistical data
NEXT STEPS
  • Study the law of total probability in detail
  • Learn about conditional probability formulas and their applications
  • Explore statistical data interpretation techniques
  • Research common pitfalls in probability calculations
USEFUL FOR

Statisticians, data analysts, healthcare professionals, and students studying probability and statistics will benefit from this discussion.

jacobson00
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am a bit confused, if i want to find out for example the P(Having the disease among everyone) , using conditional, would it be total people Having the disease over total population?Prescreening Positive and Have the disease is 66
Prescreening Positive but does not the disease 150
prescreening Negative and Have the disease is 5
prescreening Negative and does not Have the disease is 555 so if using conditional probability, i want to find.P(Having the disease among everyone)

66 +5/ total population (776)

P(Prescreening Positive for everyone)

66+150/776

Am i understanding it correctly?
 
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Hi jacobson00,

Welcome to MHB! :)

I would suggest using parentheses to be more clear, but yes I agree with your approach. There are two ways of having the disease with the way the data is arranged - either you have it and you are prescreened positive or you have it and are prescreened negative. Divide by total number of people. There isn't any overlap between the groups so it seems pretty straightforward and I agree with your answer.
 
thank you. I think i was thrown off by the term "Conditional". If looks like plain probabilities.
 
jacobson00 said:
thank you. I think i was thrown off by the term "Conditional". If looks like plain probabilities.

Well they are conditional probabilities but you are given a lot of information so you don't have to think of them that way.

You could write each of these numbers as a conditional probability and calculate the answer through the law of total probability, but that's not necessary here.

$$P[+|S^{+}], P[+|S^{-}], P[-|S^{+}], P[-|S^{-}]$$
 
Phewww! i don't think i am there yet. baby steps. Thank you
 
jacobson00 said:
Phewww! i don't think i am there yet. baby steps. Thank you

Ha, it looks scarier than it is. :) Glad you found us. Please keep posting your questions so we can help when you are stuck.
 
Regression alone enables you to do what? a) infer causality only, b) identify correlation only c) both?
 

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