Consider the following scenario: • Let P(C) = 0.4 • Let P(D) = 0.5 • Let P(C | D) = 0.6 Part (a) Find P(C AND D). Part (b) Are C and D mutually exclusive? Why or why not?   A) There is not enough information to determine if C and D are mutually exclusive. B) C and D are not mutually exclusive because  P(C AND D) ≠ 0 C) C and D are mutually exclusive because they have different probabilities. D) C and D are not mutually exclusive because  P(C) + P(D) ≠ 1 . Part (c) Are C and D independent events? Why or why not?   A) The events are independent because they are mutually exclusive. B) The events are not independent because P(C) × P(D) ≠ P(C | D) C) The events are not independent because P(C | D) ≠ P(C) D) The events are not independent because the sum of the events is less than 1. Part (d) Find P(D | C).

Q: Suppose P(A and B) = x, P(BlA) = y, and P(B) = z. What is P(A or B)?

A: According to the given information in this question We need to find the following probability

Q: If P(A) = 0.29 , P(B) = 0.32,  P(A | B) = 0.38 then P(A ∩  B) =

A: Bayes' theorem can be used to compute conditional probabilities and isexpressed as P(A|B)…

Q: Suppose P(A) P= 0.3, P(B) = 0.4 and P(A ∩ B) = 0.12. Which of the following is Correct? A) P(A U B)…

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

Q: Let S = {0, 1, 5, 4, 7}, number of subsets of S is 32Q, then find the value of Q.

A: S is a set with cardinality 5 and given he number of subsets of S is 32Q, then we have to find the…

Q: Let S = {a, b, c, d, e, f} with P(a) = 0.16, P(b) = 0.14, P(c) = 0.15, P(d) = 0.25, P(e) = 0.18, and…

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Q: 2) Show = din (2) +C

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Q: 1. Let P(A) = 0.3 and P(B) = 0.6. a) Find P(AUB) when A and B are independent. b) Find P(A/B) when A…

A: P(A) = 0.3P(B) = 0.6

Q: 2. When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and…

A:

Q: 1. Flip three coins and let Y be the number of heads that appears. Then flip Y coins and let X be…

A: Given Information: Three coins are tossed and Y is the number of heads that appear from this trial.…

Q: If A and B are independent, and the P(A) = 0.35 and P(B) = 0.45 find: a) P(A ∩ B)…

A: Given that P(A) = 0.35 P(B) = 0.45 A, B are independent events.

Q: A discount stock brokerages firm wants to know how big a sample should be taken from their customer…

A: We know that the formula for sample size is given by- Simplifying the above formula Now,…

Q: 14. Given P(A) = 0.25, P(B) = 0.28, and P(B|A) = 0.28, are A and B independent or dependent?

A: Given that: P(A) 0.25 P(B)=0.28 P(B|A) =0.28

Q: 42. If P (A) = 0.5, P (B) = 0.40 and P (A UB) = 0.70, find P (A/B) and P(A U B) where A is the…

A:

Q: Two students are named to present their work from a class of 12 students: 3 from electrical…

A: Total = 12 students  Electrical = 3  Telecom = 5 Computer = 4 2 are chosen X: Number of Electrical…

Q: 16.If A(t)=⎛⎜⎝et2e−te2t2ete−t−e2t−et3e−t2e2t⎞⎟⎠At=et2e−te2t2ete−t−e2t−et3e−t2e2t and…

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Q: 4. (4 – e 3*)³dx

A: Here we use the formula  ∫eaxdx=eaxa+C (a-b)3=a3-b3-3a2b+3ab2

Q: If X is the number of heads obtained in four tosses of a coin, the 1 is 1+X mode of Y =

A:

Q: If S= {a,b,c} with P(a)= 2P(b)= 4 P(c), find P(a)

A:

Q: If P(An B) = 0.3 find P(A U B°) O 1 0.3 0.7

A:

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

A:

Q: If P( A U B) = 0.5 , P (B) = 0.2, P (A)=0.4 then || P(B|A) Is?

A: GivenP(A∪B)=0.5P(B)=0.2P(A)=0.4

Q: 10. Let a = (1,-1,2), b = (2,0,−1), and = (3,-2,0). Evaluate or explain why the expression is…

A: The vectors:

Q: Let S = (a, b, c, d, e, f with P(b) = 0.16, P(c) = 0.12, P(d) = 0.29, P(e) = 0.22, and P(f) = 0.11.…

A: Given S = { a, b, c, d , e , f } P( b ) = 0.16P( c ) = 0.12 P( d ) = 0.29 P( e ) = 0.22 P( f ) =…

Q: 10. Show how to use Richardson extrapolation employing x, and x2 if L = x + a₁n¹ + a₂n2+an³+...

A:

Q: If P(n-1,3):P(n,4) = 1:9,Findn.

A:

Q: 1)Given P (A) = 0.25 and P (AU B)= 0.50. What must P (B) be if A and B are to be independent?

A: As per guideline expert have to answer first question only.

Q: 1. Q-1: Answer each of the following as True or False justifying your answers: 2. 1 c) If (I –…

A:

Q: If P(A) = 3/4 and P(B) = 5/6, then P(A and B) = а. %3D

A:

Q: Suppose that P(A) = 0.1, P(B) = 0.3, and P(A|B) + P(B|A) = 0.8. Find P(A ∩ B).

A: From the information, given thatThe formula of the conditional probability, for any two events…

Q: Given P(A) = 2/5      P(B) = 1/4           P(A ∪ B) = 11/20 (a) Are A and B mutually exclusive?…

A: Given information- P (A) = 2/5 P (B) = 1/4 P (A ∪ B) = 11/20 We have to check whether A and B are…

Q: If C(12,4)+C(12,5) = C(n, 5), then n is equal to

A:

Q: 3. The diagram at the right shows two different kinds of birdfeeders that are used to attract birds.…

A:

Q: Suppose A and B are independent and mutually exclusive. P(A) = 3/10. Can you determine P(B)?

A: GivenA and B are independent and mutually exclusive eventsP(A)=310

Q: Suppose that P(A) = 0.4, P(B) = 0.3 and PAUB)-042, then a. A and B are dependent b. none of the…

A: We have to find out correct answer...

Q: show that if A occurs in a larger proportion of the cases where B is than wgere B is not, then B…

A:

Q: 3. Show by an example that the following statements are false. i. a - (b c) = (a - b) (a - c) for…

A: ( i )  a - (b • c) = ( a - b ) • (a - c )  fo all a , b , c belongs to real number R   We show that…

Q: If P (A) = 0.3, P(B) =0.6, and P (Aor B) =0.7 are A and B mutually exclusive?

A: Two events are said to be mutually exclusive when both can not occur simultaneously.  A and B are…

Q: Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.25, P(d) = 0.2, P(e) = 0.1, and P(f) = 0.11.…

A:

Q: If P(A) = 0.29 , P(B) = 0.32,  P(B | A) = 0.42 then P(A ∩  B) =

A: GivenP(A)=0.29P(B)=0.32PB/A=0.42

Q: -2/=1) dz 7. Evaluate

A:

Q: 5. Given that C and D are independent and P(C | D) = 2/3        P(C ∩ D) = 1/3 find (a) P(C) (b)…

A: Given that, P(C|D) = 23 P(C∩D)=13

Q: A ∩ B = ∅, P(B) = 0.6, P(A ∪ B) = 0.6.  Find P(A).

A:

Q: Let S = {a, b, c, d, e, f} with P(a) = 0.14, P(b) = 0.24, P(c) = 0.21, P(d) = 0.15, P(e) = 0.13, and…

A: From given we have : S = {a, b, c, d, e, f} P(a) = 0.14 P(b) = 0.24 P(c) = 0.21 P(d) = 0.15 P(e) =…

Q: Suppose that P ( A ) = 0.4,  P ( B ) = 0.5 and A , B are disjoint. Compute P ( A c ∪ B c ) .

A: From the provided information, P (A) = 0.4, P (B) = 0.5 The events A and B are disjoint.

Q: 5. Use an example to explain why Vr3yP(x, y) and ayvrP(x, y) are NOT equivalent.

A: