I got this question in my hw practice set
In a class, there are 4 freshman boys, 6 freshman girls, and 6 sophomore boys. How many sophomore girls must be present if sex and class are to be independent when a student is selected at random?
I solved the number (i believe is 9) that make class and gender independent. But it got me thinking: under what scenario, can class and gender be dependent? (i mean, class and gender are totally unrelated things right? therefore, they should be independent correct?)
I tried cook up some numbers to show that they're dependent(see table below). Mathematically, I've shown, through the following table, that gender and classification are indeed dependent. But how can gender and class classification be dependent?
Male Female Total Freshman 18 20 38 Sophomore 12 16 28 Total 30 36 66