Statistics Probability - How do I do this?

In summary, To find the probability that exactly 3 out of 20 IV drug users are HIV positive, one can consider the four possible combinations of 3 positive users from the groups of light and heavy users and calculate the probability for each combination. This can be done by using the binomial distribution for the number of positive users in each group.
  • #1
pmastchief
3
0
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!
 
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  • #2
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.
 

What is the difference between probability and statistics?

Probability is the branch of mathematics that deals with the likelihood of events occurring, based on a set of assumptions. It is used to predict the likelihood of future events. Statistics, on the other hand, involves the collection, analysis, and interpretation of data to make conclusions about a population or group.

What is a random variable?

A random variable is a numerical quantity whose value is determined by chance. It represents the possible outcomes of an experiment or event, and is usually denoted by a letter such as X or Y.

What is the difference between discrete and continuous random variables?

A discrete random variable can only take on a finite or countably infinite number of values, while a continuous random variable can take on any value within a specified range. For example, the number of heads in three coin tosses is a discrete random variable, while the height of a person is a continuous random variable.

What is the difference between probability distribution and probability density function?

A probability distribution is a mathematical function that describes the likelihood of each possible outcome of a random variable. It can be represented by a table, graph, or mathematical equation. A probability density function is a continuous version of a probability distribution, used for continuous random variables. It represents the probability of a random variable falling within a particular range of values.

What is the central limit theorem?

The central limit theorem states that the sampling distribution of the means of a large number of independent and identically distributed samples will be approximately normally distributed, regardless of the distribution of the individual samples. This theorem is important in statistics because it allows us to make inferences about a population based on a sample, assuming that the sample is large enough and representative of the population.

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