Statistics Probability - How do I do this?

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SUMMARY

The discussion focuses on calculating the probability of exactly 3 HIV positive users from a group of 20 IV drug users, consisting of 10 light users and 10 heavy users. Light users have a 40% infection rate, while heavy users have a 55% infection rate. The methodology involves using the binomial distribution, specifically Bin(10, 0.4) for light users and Bin(10, 0.55) for heavy users, to determine the probability of various combinations of positive cases among the two groups. The final step is to sum the probabilities of all valid combinations of positive cases.

PREREQUISITES
  • Understanding of binomial distribution
  • Basic knowledge of probability theory
  • Familiarity with statistical notation and terminology
  • Ability to perform combinatorial calculations
NEXT STEPS
  • Study the properties of the binomial distribution
  • Learn how to calculate probabilities using combinatorial methods
  • Explore examples of probability problems involving multiple groups
  • Investigate statistical software tools for probability calculations, such as R or Python's SciPy library
USEFUL FOR

This discussion is beneficial for students new to statistics, educators teaching probability concepts, and anyone interested in understanding the application of binomial distribution in real-world scenarios.

pmastchief
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Bonus Question on Extra Credit work...

How can I do this, where do I start? I haven't taken stats before so I'm just curious to see if someone could show me how:


A study considered risk factors for HIV infections among IV drug users. It found that 40% of users who had less than or equal to 100 injections per month (light users) and 55% of users who had greater than 100 injections per month (heavy users) were HIV positive.

Suppose we have a group of 10 light users and 10 heavy users.

What is the probability that exactly 3 of the 20 users are HIV positive?



I'm interested in the methodology and the solution if possible.

Thanks for your help!
 
Physics news on Phys.org
Consider the number of choice of 3 +ve's from the groups. (0,3),(1,2),(2,1),(3,0) are the four choices possible respectively from light and heavy groups. Find the probability of each choice and add. For groups, number of +ve's follow Bin(10,0.4) and Bin(10,0.55) respectively.
 

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