Independent events or dependent events?

[duckst]

In a school, 22% of students have eye problems, 10% have hearing problems and 4% have both eye and hearing problems. Are the events of having good eyesight and having good hearing independent events? Explain your reasoning and justify your answer algebraically.

 

[LCKurtz]

We don't work your problems for you. Show us your thinking or work.

 

[pka]

In a school, 22% of students have eye problems, 10% have hearing problems and 4% have both eye and hearing problems. Are the events of having good eyesight and having good hearing independent events? Explain your reasoning and justify your answer algebraically.

Have you and your class done any work on general Independence?
For example: Have you shown that if events \(A~\&~B\) are independent then so are \(A~\&~B^c\).
If you know the proof can you prove events \(A^c~\&~B^c\) are independent?
Now I did not say they are independent, I ask if you can prove they are independent.

 

[Dr.Peterson]

In a school, 22% of students have eye problems, 10% have hearing problems and 4% have both eye and hearing problems. Are the events of having good eyesight and having good hearing independent events? Explain your reasoning and justify your answer algebraically.

I would just go with the definition of independent events. Can you state that definition? (There are a couple different ways to say it, one of which applies more directly to this problem than others, so we need to see what you have learned in order to help you find it. Or you might have a theorem that will work better than your definition.)