I had this question
"Suppose that you select a student at random from a particular college, and you record their gender and whether they prefer to use a PC or a Macintosh for their computing. Suppose that following probability P(student uses mac) = .3 , P(student uses pc) = .7, P(student is a male) = .4, and P(student is a female) = .6. Answer the following...
a.) What is the probability student is male and student is mac user if the events are independent.
b.) what is the probability student is male and student is mac user if the events are mutually exclusive
c.) what is the highest possible probability for the intersection of the events student is male and student is mac user
a.) P( mac intersects male) = .4*.3 = .12 (correct)
b.) P(mac intersections male) = 0 (correct)
c.) independent (wrong)
The reason I said independent is because it is obviously higher than mutually exclusive. Now two events with probability greater than zero that are mutually exclusive cannot be independent. So, that means if two events with non zero probabilities that are mutually exclusive are dependent. However, dependency of two events doesn't guarantee disjointedness.
There is not enough information to calculate the P(male intersects mac) when male and mac are dependent but not disjoint. That would require the conditional probability of male given mac or mac given male. I am going to talk to the professor tomorrow about this (he asked me to see him, and asked that I retry the questions and then compare them to his) but I really dont know what I am doing wrong with part C. Unless I am just misunderstanding it completely.