Q: 4 blonde boys, 6 redhead girls, and 6 boys w/ brown hair go drinking. How many girls with grown hair must join them if a student's gender and hair color are to be independent when a student is selected at random?
I've had extreme difficulty parsing these students into sets that make sense, so that I can do something like P(A|B) = P(A^B)/P(B). The confusion lies in that every "element" has two attributes with which to contend, whereas things like the roll of a die have only one attribute. Some direction would be appreciated.
It doesn't seem that it would be possible to achieve independence since all the girls are redheads, and none of the boys are. So knowing gender gives relevant information about hair color. (I.e., these characteristics are not independent.)
To achieve independence, the proportions of various hair colors would have to be the same among the girls and among the boys.