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: Pr('green' | 4 or 6) b) Use a tree diagram and apply the multiplication principle to find the…

A: Conditional Probability : Probability of event A when given B has happened P(A|B)=P(A∩B)P(B)

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: 2) Show = din (2) +C

A:

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: 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: 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: 4. Suppose that P(A)=0.7 and P(B)= 0.5, and P([AUBY) =0.1. Find a) P(AOB) b) P(A| B) c) P(B|A)

A: Given data,P(A)=0.7P(B)=0.5P(A∪B)' =0.1P(A∪B)=1-P(A∪B)'=1-0.1=0.9

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

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: 9. Let X Bin(4,.30), compute a. P(X=0) b. P(X= 1) C. P(X= 4)

A: Given that  Success of probability p=0.3 , q=1-p=0.7 Number of trials n=4 X~binomial (n,p)…

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

A:

Q: If P(E∩F)=0.042, P(E|F)=0.12, and P(F|E)=0.6, then (a)   P(E)= (b)   P(F)= (c)   ?(?∪?)=

A: It is given that P(E∩F)=0.042, P(E/F)=0.12 and P(F/E)=0.6.

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: 1. If P(A) = 0.4, P(B) = 0.5 and P(AB) = 0.3, find a) P(AB) and b) P(AUB).

A: It is given that P(A) = 0.4, P(B) = 0.5, P(A ∩ B) = 0.3

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: 5. A B Suppose that P(A)=0.4, P(B)=0.5 and P(AUB) = 0.42. Are A and B independen Yes, A and B are…

A: Given that  P(A) = 0.4 , P(B) = 0.5