Refer to Figure 2.10 to show that P(A ∩ B ∩ C) = P(A) · P(B) · P(C) does not necessarily imply that A, B, And C are all pairwise independent.
Answer to relevant QuestionsIf events A, B, And C are independent, show that (a) A And B ∩ C are independent; (b) A And B ∪ C are independent. Suppose that a die has n sides numbered i = 1, 2,···, n. Assume that the probability of it coming up on the side numbered i is the same for each value of i. The die is rolled n times (assume independence) And a “ ...A coin is tossed once. Then, if it comes up heads, a die is thrown once; if the coin comes up tails, it is tossed twice more. Using the notation in which (H, 2) , for example, denotes the event that the coin comes up heads ...A market research organization claims that, among 500 shoppers interviewed, 308 regularly buy Product X, 266 regularly buy Product Y, 103 regularly buy both, And 59 buy neither on a regular basis. Using a Venn diagram And ...A police department needs new tires for its patrol cars And the probabilities are 0.15, 0.24, 0.03, 0.28, 0.22, And 0.08, respectively, that it will buy Uniroyal tires, Goodyear tires, Michelin tires, General tires, Goodrich ...
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