If A, B, C, and D are independent events. Prove that A U B and C – D are independent.

Q: If A and B are events such that ​P(A)=0.6 and ​P(A∪​B)=0.8​, find​ P(B) when ​(a) A and B are…

A: (a)   Obtain the probability value of P(B) if A and B are mutually exclusive events. The probability…

Q: a. Assume that the selections are made with replacement. Are the events independent?

A: here use given contingency table

Q: According to special rule of addition P(A or B) = P(A) + P(B), is true if and only if a.A and B are…

A: We need to find the special rule of addition for which P(A or B) = P(A) + P(B) is true .

Q: Given P(A) = 0.3 and P(B) = 0.4, do the following. (a) If A and B are mutually exclusive events,…

A:

Q: If A and B are events such that ​P(A)equals=0.60 and P(A∪​B)equals=0.70​, find​ P(B) when ​(a) A…

A: (a)If events A and B are mutually exclusive events, then, P (A or B) = P(A)+ P(B).Or, P(B) = P (A or…

Q: Given P(A) = 0.3 and P(B) = 0.4; if A and B are mutually exclusive events, compute P(A or B)

A:

Q: Suppose A, B and C are events satisfying the following equations P(BU C|A) = P(B|A)P(C|A) and…

A: Given Suppose A, B and C are events satisfying the following equations Show that if A and C are…

Q: Suppose that A and B are non-mutually exclusive events such that 17 . P(A) = 21,P(B) = 2121 and P(A…

A: It is given that  P(A) = 8/21 P(B) = 12/21 P(A or B) = 17/21

Q: Suppose that the events A, B, and C are independents, where P(A)= 1/2, P(B)=1/3, and P(C)= 1/4. What…

A: Given that A, B, and C are independents. So,…

Q: how that if A1, A2, and A3 are independent events, then P(A1|A2 and A3)

A: Given that A1, A2, and A3 are independent events.

Q: Suppose that A, B are two events such that P(A) > 0 and P(B) > 0.  If A and B are not disjoint, then…

A:

Q: If P(A)=0.2, P(B)=0.1, and P(A∪B)=0.3, then P(A∩B)= Are events A and B independent? Are A and B…

A:

Q: If A and B are independent event then O a. P(A and B) = P(A) - P(B) %3D O b. P( A and B) = P(A) %3D…

A: Given : A and B are independent event then Correct option is C

Q: If two events are disjoint, can they be independent? If yes, give an example; if no, prove that it…

A: Independent events: Two or more events are said to be independent if the occurrence of one does not…

Q: Show that if B1, B2, and B3 are independent events then B1 and B2 U B3 are independent. Furthermore,…

A: Two events are said to be independent if the occurrence of one of them does not depend on that of…

Q: Given that A and B are independent events, show that ?̅ and B are also independent events

A: Given: Given that A and B are independent events, show that ?̅ and B are also independentevents

Q: Given P(An B') = 0.25, P(A) = 0.48 and P(B) = 0.42. Find P(A n B). Is A and B mutually exclusive…

A: (1) Let A and B are two events The known probabilities are,

Q: If A and B are mutually exclusive events then, O a. P(B) = 0, O b. P(AUB) =0 O c. P(A) = 0, %3D O d.…

A:

Q: If A and B are mutually exclusive events then, O A. P(A&B) = 0, O B. P(A) = 0, O C. P(B) =0, D.…

A: If two events, A and B are mutually exclusive then,  P(A U B) = P(A) + P(B)-P(A n B) Since A and B…

Q: Show that if events A and B obey the multiplication rule, P(A and B) = P(A) P(B), then A and the…

A: It is given that A and B follows the rule P(A∩B)=P(A)·P(B) that means the events A and B are…

Q: Show that if A and B, (n = 1,2,3, . -) are events, then An (U Bn) = U (AN Bm)

A:

Q: If A and B are mutually exclusive events then, O a. P(A) = 0, O b. P(B) = 0, O c. P(AUB) =0 O d.…

A: Two events A and B are said to be mutually exclusive when there are no common elements for both the…

Q: Let A and B be independent events with P(A) " and P(B) =. Find P(AN B) and P(A U B).

A: Given that P(A) = 1/8 P(B) = 1/5

Q: If A, B , and C are mutually exclusive events and P(A) = ; P(B) = - and P(C) = find %3D P(B' n C').

A: The events A, B, and C are mutually exclusive events.

Q: If events A, B, and C are independent, show that(a) A and B ∩ C are independent;(b) A and B ∪ C are…

A:

Q: If A and B are independent events, prove that the following pairs of events are independent: Ac and…

A:

Q: If A and B are independent event then P( A and B) = P(A) - P(B) .a O %3D P(A and B) = P(A).b O P(A…

A:

Q: If A, B, and C are three events, prove that P(ANBOC) >1– P(A)– P(B)– P(C)

A: There are three events A,B and C. So, From De Morgan's law, P(A ∪ B ∪C) = P(A∩B∩C)⇒P(A ∪ B ∪C) = 1 -…

Q: Let A, B, and C be independent events such that P[A] = 0.5, P[B] = 0.6, and P[C] = 0.1. Calculate…

A: P(A ∪ B ∪ C) = P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C) P(A) = 0.5 P(A')…

Q: If A and B are events such that ​P(A)=0.2 and ​P(A∪​B)=0.4​, find​ P(B) when ​(a) A and B are…

A:

Q: If A,B,C are mutually exclusive events with P(A) =0.25, P(B) = 0.22, P(C) = 0.75 then PAUBUC) O a.…

A: Given, A,B,C are three events with PA¯=0.25,PB¯=0.22,PC=0.75

Q: Prove: If A and B are events, then P(B) > P(A ∩ B)

A: Solution-: Given: A and B are events. We want to prove P(B)≥P(A∩B)

Q: Prove that if A and B are events, then Pr[An B] > Pr[A] + Pr[B] – 1.

A:

Q: Given P(A) = 0.5 and P(B) = 0.3, do the following: (a) If A and B are mutually exclusive events,…

A: A and B are mutually exclusive events if P(A∩B)= 0

Q: Let A and B be events of positive probability. Prove that P(A|B) > P(A) if and only if P(B|A) > P(B)

A: Let , A and B be the two events. We have , P(A)>0 and P(B)>0 i.e. both have positive…

Q: Choose the following statements that are true for any events A, B. Pr{AU B} = Pr{A} + Pr{B} –…

A: Answer - Choose the following statements that are true for any events A, B.

Q: If A and B are independant events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =

A: It is given that A and B are independent. P(A) = 0.295, P(B) = 0.32

Q: Let A and B be events with P(A) = 0.5, P(B) = 0.4. Assume that A and B are independent. Find P(A and…

A: Here the events are indepenedent P(A) = 0.5 P(B) = 0.4

Q: Given  P(A) = 0.3 and  P(B) = 0.5, do the following. (a) If A and B are mutually exclusive events,…

A: (a): Here P (A) =0.3, P(B) =0.5. Since A and B are mutually exclusive P(A and B) =0. The required…

Q: Let A, B, be two independent events such that P(A) = P(B) = 0.3 then P(A UBC) =

A: Given that PA=PB=0.3 A and B are independent events. Hence, P(A and B)=P(A)*P(B)=0.3*0.3=0.09

Q: If x and y are independent events, show that x complement and y complement are independent events.

A: It is given that x and y are independent events. That is,

Q: Show  that :If A and B are independent, it follows that the following events are also independent:…

A:

Q: If A, B, C, and D are independent event Prove that AUB and C- D are independent.

A:

Q: If E and F are two disjoint events in S with P(E) = 0.23 and P(F) = 0.6, find P(E ∪ F), P(EC), P(E ∩…

A: From the question, it is given that E and F are two disjoint events in S that is both events are…

Q: Let A, B and C be independent events with P(A)= 0.4, P(B)= 0.7 and P(C)= 0.6. Find P(A and B and C).

A: it is given that A, B and C be independent events with P(A)= 0.4, P(B)= 0.7 and P(C)= 0.6. As we…

Q: If B = A,UA,UA, UA,U.A, are mutually exclusive events, then P(B ) = Select one: O NONE P(A,)x…

A:

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: Suppose that P(A)=0.25 and P(B)= 0.4. If events A and B are mutually exclusive, find: a. P(ANB) b.…

A: Two events are said to be mutually exclusive or disjoint if both events cannot occur at the same…

Q: If A , B, C are independent events, show directly that both A U B and A \ B are independent of C.

A: Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to…

Q: Prove that if A and B are events, then Pr[A] – Pr[B] < Pr[A\ B]

A: LHS =PA-PB=PA-PA∩B In LHS, we are subtracting, therefore, the value of LHS will be small