<p><span style="font-size:18px;"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-probability-with-venn-diagrams" target="_blank">Probability with Venn Diagrams Exercise</a></span></p>
<p><strong>Note</strong>: in the video, we discussed the independent case as an "overlap" between the two circles in the Venn diagram. Unfortunately, that explanation is incomplete, because just because you have some overlap doesn't imply that the two events are independent. In fact, they are independent only when the product of the two events happening at the same time (i.e, the overlap) is equal to the product of the probabilities of the two events happening - that is, P(A and B) = P(A) × P(B). While we will formally introduce the formula in the next video or so, for now it suffices to know that just because there's an overlap doesn't mean that it's independent and that independence is a specific case of overlap in the Venn diagram (though the fact that they have that overlap implies that they cannot be mutually exclusive). </p>