Suppose A, B and C are events satisfying the following equations P(BU C|A) = P(B|A)P(C|A) and P(BUC|A°) = P(B|A°)P(C|A°) . %3D Show that if A and C are independent, then so are B and C.

Q: Suppose A and B are events with P(A) = 0.3, P(B) = 0.85, and P(B|A) = 0.6. Find the value of P(A or…

A: given data  P(A) = 0.3 P(B) = 0.85 P(B|A) = 0.6 P(A or B) = ?

Q: Let A and B be events such that P (A) = 4/10 and that P (A U B) = 7/10 Find the probability of B…

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Q: If E and F are disjoint events in which P(E)=0.25 and P(F)=D0.45, find P(E OR F).

A: If two events E and F are disjoint events thanP(E∩F)=0

Q: It is known that P(AB)=0.45, P(B)=0.90 and the events A and B are independent.                Find…

A: Independent events are events that do not affect the outcome of subsequent events.

Q: Suppose that the probability of event A is 0.3 and the probability of event B is 0.51. Also, suppose…

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Q: Suppose that P(A) = 0.26, P(B) = 0.65, and P(B|A) = 0.13. Find the probability that %3D both A and B…

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Q: If A and B are independent events such that P(A) = 0.2600 and P(A N B) = 0.2054. Find P(B). %3D

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Q: Which statement below proves A and B are independent events? P(A)=0.23, P(B)=0.62, P(A and…

A: If A and B are independent events then  P(A and B) =P(A) ×P(B)

Q: For not mutually exclusive events A and B, P(A) = 0.59, P(B)=0.46 and P(A B)=0.28. Find the P(AUB).

A: Given:        The A and B are not mutually exclusive P(A) = 0.59 P(B) = 0.46 P(A ∩ B) = 0.28

Q: The event that “A or B but not both” will occur can bewritten as (A ∩ B)∪(A ∩ B) Express the…

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Q: If E and F are mutually exclusive events with P(E) = 0.11 and P(F) 0.48, then the value of P(EUF…

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Q: Example 2.3.11 Show that for any two events A and B, P(AN B) s P(A) s P(A U B) s P(A) + P(B) nned…

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Q: Let A and B be two events such that P(A)3D0.9, P(B)-D0.5, and P (A U B) =0.6. Find: a) P(AnB) b)…

A: Disclaimer: Since you have posted a question with multiple subparts, we will solve first 3 subparts…

Q: Suppose that E and F are two events such that Pr[E] = 11/23, Pr[F] = 8/23, and Pr[EN F] = 5/23. What…

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Q: We have events A and B with P(A) = 0.4 and P(B) = 0.5. Given that P(B|A) = 0.3, find the probability…

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Q: Suppose we have three events A, B, and C. If P(A) > 0, P(B) > 0 and P(C) < 1, and we know that if…

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Q: Suppose that C and D are events such that P(C) = 4/5 and P(C&amp;D) = 3/10. Find P(D| C).

A: The formula for conditional probability is,

Q: Suppose A and B are dependent events and P(B | A)=0.4, P(ANB)=0.1, P(B')=0.62. Find P(A U B).

A: Consider that A and B are two dependent events.

Q: The rule P (E U F) = P (E) + P (F) - P (EN F) is used for: * all events disjoint events O Any two…

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Q: The addition rule P(E or F)=P(E)+P(F) applies only to which type of events? a. Complementary b.…

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Q: 2. In the diagram, AC = selected at random from AB, what is the probability that: a. X is between A…

A: Given:          AC=CBCD=DBDE=EB Let: AB=2xSo,       AB=AC+CB2x=2AC                          use…

Q: For the independent events A and B. If it is known that P(A/B) = 0.21 and P(B/A) = 0.32. then the…

A:

Q: (a) Two independent events, A and B, are such that, P(A) = 0.7 and P(B) = 0.4, calculate: (i) P(An…

A: We have to solve given problem:

Q: Consider the notation: P(E∣F)P(E∣F) Which event do we have knowledge of having already occurred?

A: The conditional probability is as below: PA|B=PA∩BPB

Q: Suppose two events E and F are disjoint.  Which of the following is true?   (1 answer) A. P(E or F)…

A: If two events E and F are disjoint then P(E and F)=0

Q: Given that P(A) = 0.47, P(B) = 0.07, and P(A and B) = 0.0329, are events A and B %3D %3D %3D…

A: Solution:- From given information p(A)=0.47p(B)=0.07p(A and B)=0.0329

Q: E, F are independent events. P(E) = 0.2, P(F) = 0.3. Find P(E ∪ F).

A: From the provided information, P (E) = 0.2 P (F) = 0.3 The events are independent.

Q: Given three events A, B, and C such thatP(A ∩ B ∩ C) Z 0 and P(C|A ∩ B) = P(C|B), show thatP(A|B ∩…

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Q: If A and B are independent events with P(A)=0.9 and P(B)=0.8, find P(A AND B).

A: It is given that , A and B are the two independent events &amp; their probabilities is P(A) = 0.9…

Q: For independent events A and B , P(A)=0.80 and P(B)=0.20, Find P(A| B)   0.8   0.2   0.3125…

A: Given  P(A)=0.80 P(B)=0.20

Q: Let A and B be events such that P (A) = 4/10 and that P (A∪B) = 7/10  Find the probability of B…

A:

Q: If A and B are any two events with P(A) = .3 and P(BIA) = .5, then the joint probability of A and B…

A: Solution-: Given: P(A)=0.3, P(B/A)=0.5  We want to find P(A and B)=?

Q: Let X and Y be the two possible events of an experiment where, p(X) = 0.5, (XUY) = 0.9 and p(Y) = p.…

A:

Q: Suppose two events E and F are independent.  Which of the following is true?   (1 answer) A. P(E and…

A: Given that two events E and F are independent.

Q: Suppose A and B are two events such that, P(A)=0.4, P(B)=0.3 and P(A and B)=0.1a.Find 푃퐴!b.Find…

A: We have the formula

Q: The PMF of the number of components K of a system that fails is defined by PK (k) = {() (0.2)*(0.8)…

A: Solution-; Let, K=be the number of components of system that fails Given: The pmf of K is,…

Q: if a and b are two events with p(a)=0.5 and p(a and b)=0.1, then P(BIA)=

A: Assume, A and B be any two events, P(A) denotes the probability of happening of event A and P(B)…

Q: Suppose events A, B, and C are independent and P(A) = + P(B) = P(C) = 1 6 %3D 4 Find the…

A: In probability, two events are independent if the incidence of one event does not affect the…

Q: Let A and B be two events such that P (A ∪ B) = 0.6 and P (A ∪ Bc ) = 0.8 Find P (A).

A:

Q: Suppose A and B are two events. If P(A)=0.5, P(B)=0.4, and P(AUB)=D0.8. Then find the P(ANB)?

A: Note : Since you have asked multiple questions, we will solve the first question for you. If you…

Q: For any two events A and B, show that P(ĀOB)=P(B) –- P(A B).

A: Answer: From the given data, A and B are any two events

Q: If P(A)=0.7, P(B) = 0.75, P(C)= 0.8, P(AUB)=Q.8, P(AUC)=0.85, P(BUc)=0.9 and P(AUBUC)=0.95. find the…

A: Given that P(A)=0.7, P(B) = 0.75, P(C)= 0.8, P(A U B)=0.8, P(A U C)=0.85, P(B U C)=0.9 And, P(A U B…

Q: Suppose that the events A, B and C are mutually independent with  P(A) = 1/2 , P(B) = 1/3, P(C) =…

A: Given A,B, and C are mutually independent P(A) = 1/2 P(B) = 1/3 P(C) =  1/4

Q: 12. Give the equations that represent each situation. For Independent Events: P(AN B) = P(A U B) =…

A: Give the equations that represent each situation

Q: Show that for two events A and B, any P(A N B) s P(A) s P(A U B) s P(A) + P(B)

A:

Q: For any event A, P (A U Ã) =1 True or false

A: for any event A, A¯  is complement of A. then A¯∩A=∅

Q: Given: the probabilities of 3 events A, B, and C, occurring P(A)=0.35 P(B) = 0.45 and P(C)=0.2.…

A:

Q: The two events E and F are independent with P(E) = 0.25 and P(F) = 0.35. Find P(E ∪ F).

A: GivenE and F are independentP(E)=0.25P(F)=0.35

Q: Show that for any events A and B, P (A ∩ B) ∪ (A ∩ B) = P(A) + P(B) − 2P(A ∩ B)

A: Given : A and B be the any events

Q: If E and F are independent events with P(E) =0.4 and P(E or F) = 0.6,then find P(F). a. 0.56 b. 0.33…

A: We have the formula for Union of two event