Statistics Probability - How do I do this?

[pmastchief]

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!

 

[ssd]

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.