Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(AN B) = 0.1. Calculate (a) P(A|B); (b) P(B|A); (c) P(A|AU B); (d) P(A|AN B); (e) P(An B|AU B).

Q: Given P(E) = 0.34, P(F) = 0.36, and P(E and F) = 0.17, what is P(E or F)?

A: Solution: From the given information,

Q: P(A) = P (B) = P(AN B)then %3D P[(AN B) U (AN B)] = 1

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Q: The probability that event A or event B will occur is

A: Given that  The probability that event A or event B will occur is P(A or B)=P(A)+P(B)−P(A or B).…

Q: Given P(E or F) = 0.82, P(F) = 0.25, and P(E and F) = 0.14, what is P(E)?

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Q: Given P(A and B) = 0.23, P(A) = 0.84, what is P(B|A)?

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

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Q: Given P(E or F) = 0.78, P(E) = 0.10, and P(E and F) = 0.18, what is P(F)?

A: Given that P(E or F) = 0.78, P(E) = 0.10, and P(E and F)=0.18

Q: P(A)=0.39P(A)=0.39, P(B)=0.36P(B)=0.36 and P(AandB)=0.25P(AandB)=0.25.P(B∣notA)=

A: It is given that, P(A)=0.39, P(B)=0.36 and P(A and B)=0.25.Let AC be the complement od the event A.…

Q: Given P(E or F) = 0.12, P(E) = 0.22, and P(F) = 0.18, what is P(E and F)?

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

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Q: Suppose A = = the event that you get 8 hours of sleep, and B = the event that you exercis If P(A) =…

A: We have given that  P(A) = 0.26 P(B) = 0.37 P(AB) = P( A and B ) = 0.11   Conditional probability…

Q: P(A|B) = 0.2, P(A) = 0.5, P(B) = 0.45                    Find P(A U B)

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Q: Does this expression P(D) = 1.4 possibly occur

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Q: Given P(A) = 0.20, P(B) = 0.25, and P(B|A) = 0.25, are A and B independent or dependent?

A: PA=0.20, PB=0.25 and PB|A=0.25

Q: Given P(E) = 0.26, P(F) = 0.48, and P(E and F) = 0.11, what is P(E or F)?

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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: 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: 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: (10 points) Let F = {{a,b}, {c, d}}. What are each of the following %3D (a) (2 points) UF (b) (2…

A: Given the set F

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?

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Q: P(A) = 0.13, P(B) = 0.47, P (A ∩ B) = 0.05 Find a) P(A|B).   b) P(B|A)

A: P(A) = 0.13, P(B) = 0.47, P (A ∩ B) = 0.05   We know :

Q: P(A) = 0.2, P(B) = 0.6, P(AUB)= 0.7 Find a) P(A|B)  b) P(B|A)

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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…

Q: P(A) = 0.4, P(B) = 0.5, P(A U B)= 0.6 a) Find P(A given B)    b) P(B|A)

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Q: Assume that P ( A ) = P ( B ). Show that A = B

A: If possible let A≠B and there is an element x ∈ A and x ∉ B Then {x} ∈ P(A) , but {x} ∉ P(B)

Q: If P(E) = 0.60, P(E or F) = 0.75, and P(E and F) = 0.10, find P(F). P(F) = (Simplify your answer.)

A: