10. Events A and B are independent, prove that any one of the following pairs A, B; A, B; A, B is independent. (Randomly select one pair to prove.)
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Q: Theorem 3-9. If A, B, C are mutually independent events then A UB and C are also ndependent.
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Q: 1! 2! 3! let A= 2! 3! 4! , det(A)= 3! 4! 5! Select one: а. 120 b. 4!*3!*2! С. 20 d. 24
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- Suppose that vehicles taking a particular freeway exit can turn right (R), or turn left.(L). Consider observing the direction for each of three successive vehicles. Which of the following sets represents the event B that at least two of the three vehicles turn left? Select one or more: O a. {(R,R,R),(R,R,L),(R,L,R),(L,R,R)} O b. { (R,L,L),(L,L,L),(R,R,L)} O C. {(L,L,R), (L,R,L), (R,L,L), (L,L,L)} O d. None of these O e. {(R,R,R),(L,L,L),(L,R,L)} O f. {(R,R),(L,R),(R,L)}f a man has five different shirts, four different neckties, and three different sport jackets, howmany different possible outfits, each consisting of shirt, tie and sport jacket are possible?fill in the blank Independent and Mutually Exclusive Events
- Let S = {c, i, p, h, e, r, s}. Let A be the set of permutations of S in which i and e appear consecutively (in the order ie). Let B be the set of permutations of S in which h and i appear consecutively. Let C be the set of permutations of S in which p and h appear consecutively. • In order to find [A], how many permutations of S are there in which i and e appear consecutively, we define a new set P and find the permutations of it. What is P and what is |P|? What is |4|? • In order to find |An B, permutations of S in which i and e and h and i appear consecutively, we define a new set Q and find the permutations of Q. What is Q and Q? What is An B? • What is [AU B|? • In how many permutations of S do either i and e, h and i, or p and h appear consecutively?An urn contains 4 balls numbered 1, 2, 3 and 4. One ball is randomly seleted from the urn. Let A = {1. 2}, B = {2, 3} and C = {3, 4}. Determine if A, B and C are pairwise and/or mutually exclusive (test all possible pairs, and all 3 together).Count the number of ways to get 12 by the 5-dice, i.e., to represent 12 = x₁ + x₂ + x3 + X4 + X5, where 1 ≤ x ≤ 6 (1+2+3+4+3 is different from 2+1+3+3+4).
- 12 A panel of Judges A and B graded seven debtors and independently awarded the following marks : - Debator 1 3 4 7 31 Marks by A Marks by B 40 34 28 30 44 38 32 39 26 30 38 34 28 An eighth debator was awarded 36 marks by Judge A while Judge B was not present. If Judge B were also present, how many marks would you expect him to award to the eighth debator assuming that the same degree of relationship exists in their judgement. SticPigeonHole principle A drawer holds a dozen brown socks and a dozen black socks, both of which are unmatched. In the dark, a man pulls socks at random. a) How many socks does he need to remove to ensure that he has at least two socks of the same color? b) How many socks does he need to pull out to ensure he has at least two black socks?If A, B and arbitrary events then show that P(A U B U C) = P(A) + P(B)+ P(C) – P(A∩B) – P(B∩C) – P(C∩A) + P(A∩B∩C)
- Which one of the following statements is False (not true)? Events A and B are independent if and only if P(A and B) = P(A) x P(B). Events A and B are independent if and only if P(A) = P(A given B). O(A) x O(not A) = 1 Events A and B are independent if and only if A and B are mutually exclusive; that is disjoint. If events A and B are mutually exclusive then, P (A or B) = P(A) + P(B).b) Events A and B are such that P(A) = 3/5, P(B) = 4/15. Find P(A U B) if i) A and B are mutually exclusive events. ii) A and B are independent events.1what are the chances that the runn ers from Detroit and Kiercrest will finish Ist and 2nd, regardless of the acler? Thae ae a runners in the finals of the district 100 mekr race. TThree of the FrUnners are from Clarksulle, two and from Linden- Kildare, oneis from Delvait, one is from hiverenest and two are rom Naud What are the Chances that the winner of the race will vbe fream Clarksuille a lik2