1. Suppose P(A) = 4/10, P(B) = 5/10, and P(AB) = 2/10. (a) Compute P(AC). (b) Compute P(AUB). (c) Compute P(A | B). (d) Compute P(B | A). (e) Compute P(B | AC). (f) Are A and B independent? Explain. (g) Are A and B mutually exclusive? Explain.

Q: LetP(A) = 0.10, P(B) = 0.20, and P(A∩B) = 0.02. Are A and B mutually exclusive? Justify your result…

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Q: Assume that P(A₁ N A₂ NA3) > 0. Prove that P(A₁ NA₂ NÃ3 Ñ A4) = P(A1)P(A2|A1₁)P(A3|A1 N A₂)P(A4|A₁…

A: We have conditional probabilitiesP() =       (i)P( =                       (ii)P( =…

Q: | 0 0 1 1 1 00011 0 0 0 0 1 5 (If the arithmetic for computing an entry involves huge powers, you…

A: As per bartleby guidelines we are allowed to do maximum of 3 subparts

Q: 7. Given P(A) = 1/3 and P(B) = 1/2 and P(A U B) = 2/3 . • (a) Find P(A¹) . . (b) Find P(A and B) (c)…

A: Given data, p(A) =13p(B)=12p(A∪B)= 23we have to find out the given probabilities.

Q: Suppose that 7 '(t) = and 7 (0) = . Find 7(t) 7(t) = <

A: Suppose that r→'t=12t,e0.2t,t and r→0=1,-1,4. Then we have to find r→t=?

Q: Let A = B = C= {x|x is a real number). Let f : A → B and g : B → C be defined as follows: f(a) = 6a…

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Q: t - 1 (a) f(t) = 1 + logs %3D V8 /8-t

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Q: 4. Let -81 | A = 1 (a) Factor A into a product PDP-1, where D is diagonal. (b) Compute e4.

A: We can solve this using diagonalisation

Q: Let B = a = The function p(t) = 2 + 4(t − 5) + 7(t − 5)², can also be written as p(t) = a + b(t − 2)…

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Q: P(A)=0.02 and p(C)=0.07 determine p(A u C), given that A and C are independent

A: It is given that:And, A and C are independent events.

Q: (c) Check whether or not: Q (2¹/³) = Q(4¹/3) Also obtain (Q (2¹/³): Q].

A: We first find [Q(2^(1/3)):Q]  Then using this prove that Q(2^(1/3))=Q(4^(1/3))

Q: Given:P(E) = 0.45, P(F) = 0.53, and P(E ∪ F) = 0.67(i) Find P(E ∩ F)(ii) Find P(F | E)a) (i) 0.31…

A: Given Two events E and F, probability of P(E) =0.45 and probability of P(F) =0.53 andP(E U F)=…

Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (2, −2, 1), v = (2, −1,…

A: Given

Q: 1) Evaluate g = Af, where A and f are given below: (a) (b) (c) (d) A SQRT d³ dr³ + x³ dx 8² 8² +…

A: The step-by-step answer is given below please check.Explanation:Step 1:a) Step 2:b) Step 3:4)…

Q: Q2 (Bayes' Theorem) It is given that P(B|A) – 0,15. P (B|A) = 0.03 and P (A) = 06. Compute P(A|B).…

A: Ac=A bar  P(B/A)=0.15, P(B/Ac)=0.03, P(A)=0.60, P(A/B)=?

Q: P(A) = 0.25, P(B) = 0.65, P(AU B)= 0.8 Find a) P(A|B)        b) P(B|A)

A: First we need to find P(AnB). P(AnB) = P(A)+P(B)-P(AUB) = 0.25+0.65-0.8 = 0.1

Q: SupposethatAandBaretwoindependenteventswithP(A) = 0.3andP(B) = 0.3. Calculate(a) P(A and B) (b) P(A…

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Q: If h(t)=t3*4 , then h(2)=?

A: Given h(t) = t^3*4 To find h(2), so here put t =2 to find the answer.

Q: P(ANB) = P(A)NP(B).

A:

Q: Consider two variables: one denotes whether a person truly has a disease (D) or not (D) and the oth…

A: Given data:   D Dc Row Total Pos 53 4 57 Neg 2 455 457 Column Total 55 459 514

Q: (c) (143)(23)(24) (k) |(1254)| (d) (1423)(34)(56)(1324) (1) |(1254)²| (e) (1254)(13)(25) (m) (12)-1…

A: Given the given expressions are a) 1345 234b)  12 1253c)  143 23 24d)  1423 34 561324e)  1254 13…

Q: Let f: AB and 9: B→C be defined as follows: f(a) = 4a² +2 and g(b) = 26-7 Compute the following: (a)…

A: Let A=B=C=x|x is a real number Let f:A→B and g:B→C be defined as  fa=4a2+2andgb=2b-7 Hence…

Q: Let r(t) = (a) Find 7 (t). (b) Find Ñ (t). (c) Find K (t)

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Q: 2t – 5, t 2

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Q: (b) 6 + 7 + 8 + 9 + ... + k

A: (b) Given that 6+7+8+9+...+k The objective is to find the sum. The formula for sum of numbers are,…

Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

A: