For Any event A, show that A And Ø are independent.
Answer to relevant QuestionsProve Theorem 2.12 by making use of the following generalization of the distributive law given in part (b) of Exercise 2.1: A ∩(B1. B2. · · · ∪ Bk) =(A ∩ B1) .(A ∩ B2) ∪ · · · ∪ (A ∩ Bk) Among the eight cars that a dealer has in his show-room, Car 1 is new And has air- conditioning, power steering, And bucket seats; Car 2 is one year old And has air-conditioning, but neither power steering nor bucket seats; ...In Figure 2.13, L is the event that a driver has liability insurance And C is the event that she has collision insurance. Express in words what events are represented by regions 1, 2, 3, And 4. If A And B are mutually exclusive, P(A) = 0.37, And P(B) = 0.44, find (a) P(A); (b) P(B); (c) P(A ∪ B) ; (d) P(A ∩ B) ; (e) P(A ∩ B) ; (f) P(A ∩ B). In a game of Yahtzee, five balanced dice are rolled simultaneously. Find the probabilities of getting (a) Two pairs; (b) Three of a kind; (c) A full house (three of a kind And a pair); (d) Four of a kind.
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