Part II: Set Relations and Probability The Venn Diagram tool in the frame below

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.

Suppose there are two events, A and B, with P(A) = 65% and P(B) = 50%. Select all that must apply. (Q13)

Problem 10 A: P(AUB)= 100% B: P(AB)215% C: A and 8 cannot be mutually exclusive D: A and B cannot be independent E: P(AUB)265% F: B cannot imply A G: A cannot implyB H: P(AUB)270% l: P(A8%50% J: P(AB),65% Suppose there are two events, A and B, with P(A) = 65% and P(B) = 50%. Select all that must apply. (Q13) K: none of the above

Explanation / Answer

Given for the two event A and B

P(A) =0.65

P(B)=0.50

Therefore, the following condition can be applied for even A and B

C) Two event A and B cannot be mutually exclusive.

D) A and B can not be independent

E) P(AUB)>=0.65 ## Since P(A)=0.65; if B is a subset of A then P(AUB)=0.65

I)P(AB) <=0.50 ## Since P(B)=0.50,

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