If the events B1, B2, ..., Bk constitute a partition of the sample space S such that P(B;) + 0 for i = 1, 2,. k, then for any event A of S, k P(A) = P(B; n A) = P(B÷)P(A|B;).

Q: 2.4 Let A and B be two events of the same sample space. If P(A|B) P(A) then the events A and B are…

A: Solution- Given that A and B are two events  P(A|B)=P(A)then the event A and B are always…

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:

Q: Let A and B be any two events defined on sample space omega.  Suppose that P(A) =.4, P(B) = .5, and…

A: The given probabilities are:P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.1.

Q: 3.if A and B are two events such that P(AUB) = P(ANB) = and P(A) = 3, then P (B) is equal to a. 1/3…

A: The question is about probability.Given probabilities are as follows :

Q: Suppose that AA and BB are two events for which P(A)=0.32P(A)=0.32, P(B)=0.73P(B)=0.73, and…

A: Given that : P(A)=0.32 P(B)=0.73     and    P(B|A)=0.37 By using the properties of basic and…

Q: TRUE or FALSE  For events A and B in a sample space, P(A|B) + P(A|Bc) = P(B).

A: Introduction: Suppose A and B are two events of interest in a sample space, with respective…

Q: Suppose A and B are two independent events with P(a)=0.5 and P(b)=0.4 what is the P(A U B)?

A:

Q: Suppose that A and B are events such that P(A) = 2/7 and P(A&B) = 3/25. Determine P(B| A).

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Q: If B CA and A and B are two events such that P (A) = 3 P (B) and A UB = S find P (B) ?

A: Answer: For the given data,

Q: In an experiment where the pointer on a wheel of chance is spun, the possible outcomes are the…

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Q: Suppose that A, B are two independent events, with P(A) = .1 and P(B) = .2. Find P(A|B).

A:

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…

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Q: Q.1 a) Given E and F are events defined on a sample space S such that P(E)=0.3, P(F)=0.5 and P (E …

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Let M and N be two events in a sample space S such that P(M) = 0.8,         P(N) = 0.4, and P(M ᴖ N)…

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Q: If the events B1, B2, ..., Br constitute a partition of the sample space S such that P(B;) #0 for i…

A:

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: Suppose E and F are events from a sample space S. What can you conclude from p(E|F)=0?

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

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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. Find…

A: We have given that  P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.9 P(A and B) = P ( A ∩ B)

Q: Show that the multiplication law P(A B) = P(A/B) P(B), established for two events, be generalized to…

A: GivenLet A and B be any two events. The conditional probability of occurrence of A given that event…

Q: Let S = {E1, E2, E3, EA} be the sample space of an experiment and let = {E1, E2}, B = {E2, E3}, and…

A: We want to find union probability of a or b

Q: In the sample space S, let P(A)=0.7, P(B) = 0.5, P(C)=0.1, P(AUB)=0.9, and P (AUB)nC|= 0.Depict the…

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Q: Q9. If A, B and C three events make partition for sample space S and D is another event in S such 10…

A: Given: P(A) = P(B) = P(C) = 1/3 P(D|A) = 10/20 P(D|B) = 9/12 P(D|C) = 8/12

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

A: Solution: From the given information, the sample space is