Suppose that we have two events, A and B, with  P(A) = 0.50,   P(B) = 0.60,  and  P(A ∩ B) = 0.40. (a) Find  P(A | B).  (Round your answer to four decimal places.) P(A | B)  =  (b) Find  P(B | A). P(B | A)  =

Q: Given P(A and B) = 0.22, P(B) = 0.75, P(B|A) = 0.84, what is P(A)?

A: Given information- P(B) = 0.75 P(A∩B) = 0.22 P(B|A) = 0.84 P(B/A) is given by-

Q: Given P(B) = 0.47, P(A and B) = 0.10, P(A or B) = 0.51, what is P(A)?

A: From the given information, the probability that occurring event B is 0.47, probability that…

Q: Suppose ℙ(?1|?2)=0.46P(E1|E2)=0.46, ℙ(?2|?1)=0.92P(E2|E1)=0.92, and ℙ(?1)×ℙ(?2)=P(E1)×P(E2)=0.24.…

A: * SOLUTION :-  From the given information the calculation is given as follows

Q: what is P(A)?

A: P(B) = 0.31, P(A and B) = 0.20, P(A or B) = 0.53

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: A student goes to the library. Let events B = the student checks out a book and D = the student…

A: Let define the events: B = the student checks out a book   D = the student check out a DVD The known…

Q: = 0.40, what is P(A)?

A: Independent event- two events ( suppose A and B) are called to be independent events if the outcome…

Q: For two events, A and B, P(A) = 0.5, P(B) = 0.5, and P(A/B) = 0.4. a. Find P(ANB). b. Find P(BIA).…

A:

Q: Given P(A) = 0.3 and P(B) = 0.4; if P(A and B) = 0.1, compute P(A or B)

A: From the provided information, P (A) = 0.3, P (B) = 0.4 and P (A and B) = 0.1

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

A:

Q: The P ( A ) = 0.5 and the P ( B ) = 0.24 . Events A and B are mutually exclusive. What is the P ( A…

A:

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: Some useful properties of set operations are as follows: (proofs may be as exercise) Commutativity:…

A: There are 4 useful properties are given ,  Commutativity Associativity  Distributive laws De…

Q: The two events E and F are independent with P(E) = 0.45 and P(F) = 0.3. Find P(E ∪ F).

A: Given that, The two events E and F are independent with  PE=0.45 PF=0.3 The probability PE∪F is…

Q: Given P(B) = 0.29, P(A and B) = 0.27, P(A or B) = 0.48, what is P(A)?

A: Given, PB=.29PA and B=PA∩B=.27PA or B=PA∪B=.48 We have, PA∪B=PA+PB-PA∩B⇒   PA=PA∪B+PA∩B-PB…

Q: Given P(A and B) = 0.11, P(B) = 0.41, P(B|A) = 0.79, what is P(A)?

A: Given, P(A and B) = 0.11 P(B) = 0.41 P(B|A) = 0.79 P(A)=?

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: C and D are events with P(C) = 0.4 and P(D) = 0.5 and P(C|D) = 0.6.For each part, show how you…

A: From the provided information, P (C) = 0.4 and P (D) = 0.5 And P (C|D) = 0.6

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

A:

Q: Given P(B) = 0.47, P(A and B) = 0.21, P(A or B) = 0.40, what is P(A)?

A: P(B) = 0.47 P(A and B) = 0.21 P(A or B) = 0.40

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: The events A and B are independent. P(A)=2x, P(B)=3x, P(AUB)=2/3). Find the value of x.

A: Given Data: P(A)=2x P(B)=3x P(AUB)=2/3 The probability of A intersection B is, PA∩B=PA·PB=2x3x=6x2

Q: Given P(A and B) = 0.18, P(B) = 0.78, P(B|A) = 0.82, what is P(A)?

A: Given information- P (B) = 0.78 P (A∩B) = 0.18 P (B|A) = 0.82 P (B/A) is given by-

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…