3. If A, B and D are three events in a sample space where An B = 0 and AU B = S, show that P(D) = P(D|A)P(A) + P(D|B)P(B) 4. If A and B are two events, prove that P(B|A)P(A) P(A|B) : P(B|A)P(A) + P(B|A)P(A)

Q: 1. Let A and B are two evens of a sample space S and let P(A)=0.5, P(B)=0.7 and P(AUB)=0.9. i) Find…

A: Given,P(A)=0.5P(B)=0.7P(A∪B)=0.9

Q: Each of three persons fires one shot at a target. The outcomes of the shots made by them are…

A: Using the provided information, it is to be tested, if the given events, i.e., A1, A2, and A3 are…

Q: Let Ω={1,2,3,4,5} be the sample space of a random experiment. Let also the events A={1,2} and…

A:

Q: Suppose A and B are events of a sample space. Assume that P (A) = .45 P(B) = .30 P(A∪B) = .55…

A: Suppose A and B are events of a sample space. Assume that P (A) = .45 P(B) = .30 P(A∪B) = .55…

Q: 2. Suppose that A, B, C are mutually independent events in the sample space of some random…

A: 2) Given that A, B, C are mutually independent events in the sample space of some random experiment,…

Q: Let A and B are two event of a sample space S and let P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.9 Are A…

A: We will use the union formula: P(A∪B)=0.9 P(A)+P(B)-P(A∩B)=0.9 0.5+0.7-P(A∩B)=0.9 P(A∩B)=0.5+0.7-0.9…

Q: (1) For any two events A and B in a sample space S, if BCA, then P(A|B)=1.

A:

Q: 2. Let A and B be two events with P(A) = and P(B) = . Show that %3D (a) P(AU B) > 3/4 (b) 를<P(An B)…

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

Q: Let A, B C N be events in a sample space such that P(A) = .45, P(B) = .67, and P(ANB) = .23. Compute…

A: It is given that, P(A) =0.45 P(B) = 0.67 P(A∩B) =0.23

Q: 3. A and B are two events of the sample space S = {1, 2, 3, 4, a, b, c, d}. If A = {2, 4, c, d} and…

A: I solved exactly first three subparts because of bartleby policy. If you want more please uplode…

Q: Identify whether the given hypothesis is null or alternative. If it is an alternative hypothesis,…

A: The training group scores will not be different from the control group scores

Q: Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(AIB) = 0.1 Then P(A|AUB) is

A: Given that Two events A and B  P(A)=0.5 P(B)=0.3 P(A/B)=0.1 We have to find P(A/AUB)

Q: b) Given A and B are independent events, with P(A) = 0.50 and P(B) = 0.30. Find P(ANB)

A:

Q: at random events A and Bare independent, A and C are independent, and BC = 6. %3D P(B) =,P(AC |…

A: Given that

Q: 1. An event outside the sample space has a probability approximately equal to zero. TRUE FALSE

A: Defination Sample space: Sample space may be defined as the total possible outcomes.  Note:…

Q: Given two cvents A and B that are defined on the same sample space 2. Decide whether the following…

A: I). The statement "PA∩B=PA.PB" is sometimes true when the events  A and B are independent of…

Q: 2) Suppose A and B are events such that P(A) = 0.6, P(B) = 0.7 and P(A or B) = 0.8. Calculate the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: 2. If A and B are two events defined on the sample space Q, then P(A U B) ≤ P(A)+P(B) always. O TRUE…

A: If A and B are two events defined on tha sample space,then P(A U B)≤P(A)+P(B) Answer True

Q: Let A and B are two evens of a sample space S and let P(A)=0.5, P(B)=0.7 and P(AUB)=0.9. i) Find the…

A: Given,P(A)=0.5P(B)=0.7P(A∪B)=0.9

Q: 2 Suppose A and B are events in a sample space Q and that P(A) = , P(B) = ; and P(AN B) -) P(A|B) >)…

A: Given that PA=25P(B)=13P(A∩B)=110 c) P(A'|B)=P(A'∩B)P(B)               =P(B)-P(A∩B)P(B)…

Q: 8. Two events, A and B, are such that P(A)=.45,P(B) = .65,Pl B)=.25, determine PBN

A:

Q: Let A and B be two events with P (A) = 1/2 and P (B ^ c) = 1/4. The only thing we can say for sure…

A: It is given that A and B are two events. Therefore,

Q: Let A, B, and C be three events of the sample space S such that n(S)=60, n(A)=30, n(B)=18, n(C)=36…

A: Given The data is as follows: n(S)=60 n(A)=30 n(B)=18 n(C)=36

Q: If A and B are two independent events in a sample space S, find weather the following statement is…

A: GivenA and B are independent then (Ac , Bc) and (A,Bc)  also independent

Q: Let S be a sample space and two mutually exclusive events A and B be such that AUB = S. If P(-)…

A: Given that S is a sample space and A and B are mutually exclusive events.

Q: Box 1 (B1) has 3 Red and 4 Green balls, Box 2 (B2) has 4 Red and 5 Green balls. One of the boxes is…

A: given that box1 has 3 red and 4 green balls box2 has 4 red and 5 green balls ( a )P(R)=? (b)P…

Q: 1. Suppose A and B are events in a sample space 2 and that P(A) = , P(B) = ; and P(AN B) = Calculate…

A: Given - let A  and B are events in a sample space . P(A) = 25    P(B) = 13 and  P ( A ∩ B) = 110 To…

Q: (5) If two events A and B are mutually exclusive, then the joint events, AnC and BOC are also…

A:

Q: The following two-way table shows the distribution of daily traffic and weather issues in a certain…

A: Given :

Q: Let (S, P) be a sample space where S = (1,2,3,..., 10} and P(j) = j/55 for j = 1,2,.., 10. Let A be…

A:

Q: 23. Let A and B be events of a sample space of an experiment, if P(QE =P(BIB) then value of P(Q|B)…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: 1. Let S represent the sample space. A and B are two events in the sample space, S. If S = {x | 2< x…

A: As per guideline expert have to answer first question only.

Q: Let A and B be independent events defined on the same sample space such that P(A U B)= 0.6 and P(B)…

A: Given ,P(AUB)=0.6P(B)=0.2and A, B  are independent events.

Q: Let Ω={1,2,3,4,5} be the sample space of a random experiment. Let also the events A={1,2} and…

A: A = {1,2} B = {2,3,4} A∩B = {2} [elements in A and b] A∩Bc = {1} [ Belongs to A but does not belongs…

Q: Which of the following rules about probability is not correct? a) If event A and event B are…

A: The objective of the question is to identify the incorrect rule among the given options related to…

Q: Let A and B be events in sample space having positive probability. (a) If P(A|B) < P(A), show that…

A: According to guide lines we are supposed to solve the first three subpart only rest can be…

Q: Let A and B be two arbitrary events in a sample space S. P(A'|B) + P(A|B) = ? a. o. P(A|B') + P(A’|…

A: P(A'|B)+P(A|B)

Q: 1 Given that A and B are two events where P(A) = , P(B') = 3 Find P(AUB) =: 4 (a) P(AOB) (b) P(A|B)…

A: Note: Please repost part d as I can author only 3 sub-parts as per my policy Given…

Q: Suppose that E and F are two events and that P(E)=0.8 and P(F|E)=0.5. What is P(E and F)​?

A: Given data,  P(E)=0.8  P(F|E)=0.5 P(E and F)​=?

Q: you say about P(B)?

A:

Q: If we throw a coin (3) times , the event(A) represent appearance (H) twice ,and the event of( B)…

A:

Q: Let A and B are two event of a sample space S and let P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.9 .…

A: For any two events A and B, it is known that P(A ∪ B) = P(A)  + P(B) – P(A ∩ B).

Q: Let A and B be events in a sample space with positive probability. Prove that P(B|A) > P(B) if and…

A: