Let A and B be events such that 0

Q: Let A, B be two mutually exclusive events such that AUB = 2, p(A) = 4p(B). Find p(B - A) Select one:…

A:

Q: Let A and B be two events such that P(A) = 1/7, P(AUB) =1/2, and P(AB) =1/2  Determine P(B)

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Q: let A ,B be two disjoint events such that P(B) = 0.1 then P(A° \ B ) = 1 0.5 Other

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Q: 1. Let A and B be events such that, P(A) = 0.6, P(B) = 0.7, P(A N B) = 0.4 Find %3D a. P(A U B) b.…

A: Given that, A and B are events, PA=0.6PB=0.7PA∩B=0.4

Q: Let A and B be events with P(A) = 0.1 and P(B) = 0.4. Assume that A and B are independent. Find P(A…

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Q: Let A and B be events such that P(A) = 0.5, P(B) = 0.4 and P(A∪B) = 0.6 .     Find P(A|B)

A:

Q: Determine whether E and F are mutually exclusive, if E is the event "being a plumber", and F is the…

A: Mutually exclusive means when two events can not occur at the same time.

Q: Let A and B be events such that: P(A) = 0.5, P(B) = 0.6, P(A∩B) = .4a. P(A ∪ B) =b. P (A|B) =c.…

A: It is given that:

Q: Let E and F be two events in S with P(E) = 0.39, P(F) = 0.4, and P(E ∩ F) = 0.22. Find P(EC ∩ F) and…

A: To compute the probabilities of the required events , using addition and complementation laws

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 such that P(A) = 0.45 and P(B)=0.35. Then P(A and B)= %3D…

A: Given that P(A) = 0.45 P(B) = 0.45 And given that A and B are mutually exclusive events

Q: Let A and B be events such that P(A) =1/8, P(A or B)=1/6 and P(A and B)=1/11. Determine P(B)

A: P(A) =1/8, P(A or B)=1/6,  P(A and B)=1/11.

Q: Let A, B be two events such that P(A) > 0 and 0 < P(B) < 1. • (i) Define P(A|B). • (ii) If P(A) <…

A: a) Conditional probability is a measure of the probability of an event occurring, given that another…

Q: Show that if E1,... , En are events such that P(E;) = 1 for i = 1, ...,n, then Ek) = 1. k=1

A: We have events E1, E2,...., En such that PEi = 1. We have to that the probability of the event…

Q: Let A, B and D be events. Show that p(A ∪ B|D) = P(A|D) + P(B|D) − ?(A ∩ B|D).

A:

Q: 10. Let A and B be events such that Pr[B] = 0.7,Pr[A U B] = 0.9, Pr[A|B] = 0.3. Find Pr [A]. %3D %3D

A: Provided information: P(B)=0.7P(A∪B)=0.9P(A|B)=0.3

Q: 1. Let A and B be two events such that P(A) = 0.4, P(B) = 0.7, P(A U B) = 0.9 %3D a) Find P(A n B).

A: Given: P (A) = 0.4 P (B) = 0.7 P (A U B) = 0.9   a) P (A ∩ B) = ?

Q: Suppose that A and B are events such that P (A|B) = P (B|A) , P(AUB) = 1, and P(An B) > 0. Prove…

A: Solution: From the given information,

Q: Let A and B be events where P(A) = 1/3 and P(B) = 1/4. Show bounds for P(A intersection B)

A: P(A) = 1/3, P(B) = 1/4.

Q: Let A and B be two events such that P(A/B) = P(B/A) = and P(An B) = 1/ 1 Then P(AUB) = 2/3 3/4 1/3 O…

A:

Q: Let A and B be mutually exclusive events with P(A)=0.43 and P(B)= 0.53 calculate P(A ∩ B)…

A: From the provided information, P(A) = 0.43, P(B) = 0.53

Q: Finite: If A and B are events such that P(A)=0.5 and ​P(A∪​B)=0.9​, find​ P(B) when ​(a) A and B…

A: Given that, Let A and B are events such that P(A)=0.5 and ​P(A∪​B)=0.9

Q: Let A and B be events such that Pr[A]=0.37, Pr[B]=0.62, and Pr[A N B]=0.11. Find Pr[A|B].

A:

Q: Let A and B be events where P(A) = 1/3 and P(B) = 1/4. Show bounds for P (A U B) and P (A…

A:

Q: Let A and B be two events such that P(A)=1/7, P(AUB)=1/2, and P(AB)=1/12. Determine P(B)

A: From the provided information, P (A) =1/7 P (A Ս B) = 1/2 And P (AB) = 1/12

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: 2. Let 0 0, P(B| A) = P(B|A), then that event A and B are independent. prove

A: We need to prove, P(AnB) = P(A)P(B)

Q: Let A and B be events such that P (A) = 1/5 P (A & B) = 1/10 and P (A or B) = 1/2 Determine P (B)

A: P(A)=15P(A and B) = 110P(A or B) = 12

Q: If A and B are two disjoint events such that p(A) = 0.3 and p(B) =0.2, then p(AU B) = %3D %3D Select…

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Q: 5. Let A and B be events such that 0 < P(A) < 1 and 0 < P(B) < 1 a. Show that if A and B are…

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Q: Let A and B be events such that​ Pr[A] =0.370.37​, Pr[B] =0.630.63​, and​  Pr[A ∩​ B] =0.240.24.…

A: Required to calculate the conditional probability that A occurs given B has occured, P(A|B)

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)=0.5 and P(B) =0.3 a) if A and B are mutually exclusive events, compute P(A or B)

A: Two events are said to be mutually exclusive events, if two events can not occur simultaneously.…

Q: If A and B are disjoint events such that P(A) = 0.35 and P(B)=0.50. Then P(A U B)= O a. 1 O b. 0.85…

A: Disjoint events cannot happen at the same time. In other words, they are mutually exclusive.

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: Let A and B be events such that​ Pr[A] = 0.43​, ​Pr[B] = 0.54​, and​ Pr[A ∩​ B] = 0.23. Find ​…

A:

Q: Let A, B, and C be mutually exclusive and exhaustive events such that P(A)=0.4 and P(A U B) = 0.5.…

A: let A,B and C be mutually exclusive and exhaustive events such that P(A)=0.4 and P(A∪B)=0.5find…

Q: Let A and B be events such that P(A)=0.5, P(B)=0.4 and P (A U B) = 0.6 Find P (A/B). Probability =

A: Formula : P(A|B) = P(AnB)/P(B) P(AuB) = P(A) + P(B) - P(AnB )

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: Let E and F be event such that P(F) = 0.6, P(E|F) = 0. 5 and P(E|F ) = 0. 3 Find P(F|E) =?

A:

Q: If A and B are disjoint events such that P(A) = 0.30 and P(B)= 0.40 then P(BNAC) = O 0.40 O 0.50 O…

A: Given: A and B are disjoint sets. PA=0.30PB=0.40PA∩B=0 PB∩Ac is obtained as below:…

Q: Let A and B be events with P(A) = 0.1 and P(B) = 0.4. Assume that A and B are independent. Find P(A…

A: We have given that,  A and B are two independent events with     P(A) = 0.1 and P(B) = 0.4 Then, We…

Q: Let A and B be events where P(A) = 1/3 and P(B) = 1/4. Show bounds for P (A U B)

A: Given ,PA=13 , PB=14We know that PA∪B≥PB                    PA∪B≥PA              and PA∪B≤PA+PB

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

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: Prove that if E1, E2,.., En are independent events, then P(E, U E2 U .. U En) = 1- | 1– P(E;)] i=1

A: Given that, E1, E2, ........., En are independent events. We need to prove that: P(E1∪E2 ∪…