In a class there are 4 freshman boys, 6 freshman girls, and 6sophomeore boys. Co
ID: 2914244 • Letter: I
Question
In a class there are 4 freshman boys, 6 freshman girls, and 6sophomeore boys. Consider theevents: A={astudent is a girl} B={a student is a sophomore} How many sophomore girls must be present if the events A and Bare to be independent? In a class there are 4 freshman boys, 6 freshman girls, and 6sophomeore boys. Consider theevents: A={astudent is a girl} B={a student is a sophomore} How many sophomore girls must be present if the events A and Bare to be independent?Explanation / Answer
If there are zero sophomore girls then if event A happens {astudent is a girl}, then it is necessarily true that event B does NOT happen. So in that case event B is dependent on event A. (so they'renot independent) Now consider if there is 1 sophomore girl. Then if A happens, then B may or may not happen (it could be the 1sophomore girl, or it could be one of the 6 freshman girls) If B happens, then A may or may not happen (it could be the 1sophomore girl, or it could be one of the 6 sophomore boys). So in this case neither event depends on the other - so they areindependent. All you need is one soph. girl.