(b) Suppose that the experiment A has M mutually exclusive possible out- comes Am, and the experiment B has N mutually exclusive possible out- comes Bm. Then, show that we P(Bn|Am) may be expressed in terms of P(Am|Bn) and P(Bm) by the relation P(Am|Bn)P(Bn) E-1 P(Am|B;)P(B;) P(B„|Am) The is relation is known as Bayes' rule.

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Q: (c) P(\X| > 3) (d) P(|X – 5| > 3)

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A: The probabilities of the events are given as follows:

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Q: 2. LetG = (Z12,) & H == {4,8,0}. Then [G:H]=3. *True *False

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Q: Let G be a a gsoup psove that CGIG)-1and (G:le))-IGI-

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Q: .

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Q: a) Let f and g be defined as fƒ\x² = x - 5 and gx=x²-1 f 1. f+g 2. f-g 3. fog 4. 5. g g f . Find,

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Q: 2. Suppose A and B are independent. If Pr[AU B] = .6 and Pr[A] = .4, find Pr[AN B']. %3D

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Q: Suppose [V]s₁ =2]. If B₁ = { [2] [3]} ² and B₂ and B₂ = { [ ₁ ] [ 3 ] } find [v] [V] B₂ = =

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