Probability help

[matthewicee]

How would I solve this?

 

[JeffM]

On what basis do you assert that they are independent?

 

[Dr.Peterson]

View attachment 19489
How would I solve this?

I presume "are independent" is given in the problem, and you just have to assume it; I'd feel better if it said something like "are found to be independent", to avoid giving the impression that it is obvious, or even reasonable. I notice that the problem also doesn't identify the population surveyed. (I also find "identify" an odd word to use there ...)

But setting aside those issues in the problem statement, if I told you that P(S) = 0.32 and P(C) = 0.41 and that S and C are independent events, how would you find P(S | C) and P(S ∩ C)? Do you know any formulas for these?

Some people would find P(S | C) first, and others would find P(S ∩ C) first. You can do either. But if you understand what independence means, the former is obvious. So, what does it mean?

 

[pka]

View attachment 19489How would I solve this?

If events \(C~\&~D\) are independent then \(\mathcal{P}(C\cap D)=\mathcal{P}(C)\cdot\mathcal{P}( D)\) therefore \(\mathcal{P}(C| D)=\mathcal{P}(C)\).
Therefore the answers above are trivial.