Part II: Set Relations and Probability The Venn Diagram tool in the frame below
ID: 3051267 • Letter: P
Question
Part II: Set Relations and Probability The Venn Diagram tool in the frame below is designed to help you visualize the relations between sets, but it will only plot rectangular sets. Unless a question specifically refers to the tool, you should consider what would happen with other shaped sets as well in answering the questions Click the radio button to highlight the event "A or B." Drag the events A and B around with the mouse. Notice how the probability of "A or B" varies as you do. Do not change the probability of A or of B until instructed to do so! Make sure that you have not changed the probability of A or of B: you should have P(A)-30% and P(B)-20% Now experiment with changing the probabilities of A and B and dragging A and B around; try to make P(AB) as large as possible and as small as possible. Think about what could happen in general, not necessarily for rectangular events; that is, suppose we specify P(A) and P(B), but neither the shapes nor the positions of A and B Problem 10 Suppose there are two events, A and B, with P(A) = 62% and P(B) = 51% A and B cannot be mutually exclusive b: P(AUB)=100% C: B cannot imply A D: P(AUB)267% E: P(AB)S5196 F: A and B cannot be independent G: P(ABR 13% H: A cannot imply B l: P(AB)s62% J: P(AUB)262% K none of the above Select all that must apply. (Q13)Explanation / Answer
The following statements are true and must apply:
A. A and B cannot be mutually exclusive as P(A) + P(B) > 100%
E. P(A and B) <= 51% (Size of B)
G. P(AB) >= 13% for P(AUB) <= 100%
H. A cannot imply B as P(A) > P(B)
J. P(A U B) >= 62% (Larger of A or B)