C1. Let 2 be a sample space with a probability measure P, and let A, B C be events. For each of the ollowing statements, state whether the statement is true or false (that is, always true or sometimes False). If it is true, briefly justify the statement; if it is false, give a counterexample. (a) If P(A) ≤ P(B), then A C B. (b) P(An B) + P(An Bc) = P(A). (c) P(AUB) ≤ P(A) (d) If A and B are disjoint, then P((AUB)) = 1 - P(A) – P(B).

Q: If A denotes some event, what does A denote? If P(A) = 0.992, what is the value of P(A)? What does A…

A: Solution: Let A be the some event.  P( A)= 0.992

Q: A woman decides to have children until she has her first girl or until she has four children,…

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Q: q10- Two events A and B are said to be independent if: Select one: a. P(A ∩ B)= P(A)*P(B) b. All…

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Q: Defective components: A lot of 9 components contains 4 that are defective. Two components are drawn…

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Q: Assume that we have two events A and B, that are mutually exclusive. Assume further that P(A) = 0.35…

A: Two event called mutually exclusive if p(a and b)=0

Q: Let event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math…

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Q: 2b) Find zo for the following probabilities: Zo ii) P (z ≤ Zo) = 0.30 0.52 0.12 0 -0.52

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Q: 11.) Rewrite each of the following percentages as probabilities, or p levels: 11a.) 17% 11b.)…

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Q: In how many different order could the police department arrange six suspects in a police lineup if…

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Q: Supposed P(F) = .25, P(F or G) = .70, and events F and G are mutually exclusive.  Find: a) P(G)…

A: (a)If events F and G are mutually exclusive, then, P (F or G) = P(F)+ P(G).Or, P(G) = P (F or G) –…

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Q: For the following, state whether the events created are mutually exclusive and collectively…

A: It is needed to define whether the event is mutually exclusive or collectively exhaustive

Q: If A denotes some event, what does A denote? If P(A) = 0.008, what is the value of P(A)? What does A…

A: Given data: If A denotes some event, what does A' denote? If P(A) = 0.008, To find: what is the…

Q: A AC Total B 0.443 0.005 0.528 BC 0.224 0.24 0.427 Total 0.667 0.333 1

A: From the cross-tabulation table, we have P( A ) = 0.667 P( B ) = 0.528 P( Ac and B ) = P( B ) - P( A…

Q: Let event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math…

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Q: If A and B are independent events, prove that the following pairs of events are independent: Ac and…

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Q: If P(A) = 0.4, P(B) = 0.2, and P(A and B) = 0, which of the following is true?   A. Events A and B…

A: given data,p(A)=0.40p(B)=0.20p(A and B)=0which statement is true=?

Q: (a) The probability that you get all Limes. (b) The probability that you get exactly 2 Lemons. (c)…

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Q: 6a. Supposed P(A) = .45, P(B) = .24, and events A and B are mutually exclusive. Find... a. P(A or…

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Q: Let A and B be events such that P (A) = 4/10 and that P (A∪B) = 7/10  Find the probability of B…

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Q: 1.) Please find the following probabilities of A, B, C? A.) ?(? ≤ −1.2)= B.) ?(? ≥ 0.08) = C.)…

A: Given: A.) P(Z ≤ −1.2) B.) P(Z ≥ 0.08)  C.) P(0.23 ≤ Z ≤ 1.40)

Q: Let A and B be events in a sample space with positive probability. Prove that P(B|A) > P(B) if and…

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Q: Let A and B be any two events defined on S. suppose that p(A)=0.2, p(B)=0.7, and p(A and B)=0.3, the…

A: It is given that, p(A) =0.2 p(B) =0.7 and p(A and B) =0.3

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Q: P(A) = 0.4 and P(B) = 0.5. Complete parts (a) through (d). Suppose that events A and B are disjoint,…

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Q: Q5A A box contains 68 red balls, 80 white balls, and 55 blue balls. (a) If one ball is drawn from…

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