Show that (a) if P(A) = P(B) = P(AB), then P(ABUBA) = 0; (b) if P(A) = P(B) = 1, then P(AB) = 1.

Q: If A × B ={(p, q),(p, r), (m, q), (m, r)},     find A and B.

A: A will be the set of the first ordinates  And B is the set of the second ordinates

Q: If n(A) = 2, n(B) = 5, and n(A ∪ B) = 7, find n(A ∩ B).

A:

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: If n(A) = 45, n(B) = 15, and n(A ∩ B) = 9, find n(A ∪ B).

A:

Q: 1. Suppose P(A) = 4/10, P(B) = 5/10, and P(AB) = 2/10. (a) Compute P(AC). (b) Compute P(AUB). (c)…

A: As per our guidelines we are suppose to answer only three sub parts.…

Q: If S = {a, b, c} with P(a) = 4P(b) = 3P(c), find P(a).

A:

Q: If n(A ∪ B) = 97 and n(A) = n(B) = 66 find n(A ∩ B).

A: Given, n(A ∪ B) = 97 and n(A) = n(B) = 66

Q: If S = {a, b, c} with P(a) = 8P(b) = 2P(c), find P(a).

A:

Q: hat p (A) =0.3 and P (B) = 0.2 find P (A or B) given that (a) A and B are mutually exclusive, (b) A…

A: p (A) =0.3 and P (B) = 0.2  (a) A and B are mutually exclusive P (A or B) = P(A) + P(B)…

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

A:

Q: If n(A) = 40, n(B) = 22, and n(A ∩ B) = 4, find n(A ∪ B).

A: topic - sets

Q: If n(A) = 41, n(B) = 15, and n(A ∩ B) = 2, find n(A ∪ B).

A: We will use the following n(A U B) = n(A) + n(B) - n(A ∩ B)

Q: Given that A and B are independent with P(A ∪ B) = 0.8 and P(B c ) = 0.3, find P(A).

A:

Q: If S = {a, b, c} with P(a) = 8P(b) = 5P(c), find P(a).

A: Total probability:If a sample space contains mutually exclusive and exhaustive events, then the sum…

Q: 18

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

A:

Q: If P(A) = 0.4, P(B) = 0.9, \ and P(An B) = 0.3, \ then (a) P(A|B) = \ and (b) P(B|A) =

A: We have to find given probability...

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

A:

Q: If P (B) = 1/4, P (A ∪ B) = 1/2 and P (A|B) = 2/3, then which of the following statements is true?…

A: GivenP(B)=14P(A∪B)=12P(A|B)=23

Q: Given P(A) = 0.22, P(B) = 0.24, and P(B|A) = 0.21, are A and B independent or dependent?

A: We know,  P(B/A) = P(A∩B)/P(A)     P(A∩B) = P(A) P(B) Events A and B are independent if the equation…

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

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Q: Given P(A) = 0.21, P(B) = 0.24, and P(B|A) = 0.24, are A and B independent or dependent?

A:

Q: If n(A) = 62, n(B) = 19, and n(A ∩ B) = 4, find n(A ∪ B).

A:

Q: Given P(A) = 0.27, P(B) = 0.27, and P(B|A) = 0.21, are A and B independent or dependent?

A: Events A and B are said to be independent if P(A∩B)=P(A)·P(B) Given:  P(A) = 0.27, P(B) = 0.27, and…