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)

Q: A car can travel from Town A to Town C by using the four roads below. The probabilities of these…

A: If occurrence and non occurrence of a event does not depend upon the occurrence and non occurrence…

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: A car can travel from Town A to Town C by using the four roads below. The probabilities of these…

A: Given information: A car can travel from Town A to Town C by using the four roads. Probability of H1…

Q: Show that the conditional probability P (A | B) of events A and B satisfies the three axioms of a…

A: Answer: -From the given data, conditional probability P(A|B) of events A and B.

Q: 7. Let A and B be events such that P(A) = } = P(B) and P(AªNBº) = . Find the probability of the…

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Q: A computer-consulting firm presently has bids out on two projects. Let A= [awarded project 1] and B=…

A: Given: PA=0.75, PB=0.35 and PA∩B=0.2.

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)

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Q: let A and B be two events in an outcome space M such that M = A U B, P (A) = 0.65 and P (B) = 0.75.…

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Q: 1. Let A and B be independent events such that P(A), P(B) > 0. Is it possible that A and B are…

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Q: Assume that A and B are random events such that 0<P(A)<1 and O<P(B)<1. Therefore it is fulfilled:…

A: Given that  A and B are random events such that 0&lt;P(A)&lt;1 and O&lt;P(B)&lt;1. We have P(A and…

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 V be the event that a computer contains a virus, and let W be the event that a computer contains…

A: Given Data: P(V)=0.12 P(W)=0.63 P( V and W)=0.04

Q: Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a…

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Q: Let A, B and C be three independent events such that P(A)= P(B)= 0.3 and P(C)=0.5. Find the…

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Q: Let V be the event that a computer contains a virus, and let W be the event that a computer contains…

A: Given: Let V be the event that a computer contains a virus and Let W be the event that a computer…

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

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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 E be the event that a corn crop has an infestation of ear worms, and let B be the event that a…

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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, each with positive probability. a. State inwords what it means for event B to…

A: Note: Hey, since multiple sub parts are posted, we will answer first three sub parts according to…

Q: a. What is P(Xi= 1, X2= 1), that is, the probability that there is exactly one customer in each…

A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks   Given :

Q: Compute the probability of each of the following events (i) X <1 1/2 (ii) XY is even

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Q: A car can travel from Town A to Town C by using the four roads below. The probabilities of these…

A: the probability that a car cannot reach Town C from Town A = P(H1) * P(H2) * P(H3) * P(H4)

Q: uestion 16 For any two events A and B to be not independent, P(AN B) = P(A).P(B) True False

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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: Let V be the event that a computer contains a virus, and let W be the event that a computer contains…

A: Given : Let V be the event that a computer contains a virus P(V) = 0.48  Let W be the event that a…

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: (b) When a soldier fires at a target, the probability that he hits the 1 target in - for solider A,…

A:

Q: Let V be the event that a computer contains a virus, and let W be the event that a computer contains…

A: It is given that the event V represents the computer contains a virus and the event W represents the…

Q: In a certain factory, machines I, II, and III are all producing springs of the same length. Machines…

A: Obtain the probability that it is defective if one spring is selected at random from the total…

Q: Let A and B be any two events defined on S. suppose that p(A)=0.2, p(B)=0.7, and p(A and B)=0.3, the…

A: It is given that, p(A) =0.2 p(B) =0.7 and p(A and B) =0.3

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, 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, 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: If P(E) = 0.2, P(F) = 0.3, and E and F are independent events, find P(E and F). 1) 0.06 2) 0.08 3)…

A: Given : p ( E ) = 0.2 p ( F) = 0.3

Q: 1. Let A and B be random events. Show that if AC B then P(A)<P(B).

A:

Q: A car can travel from Town A to Town C by using the four roads below. The probabilities of these…

A: The cases in which the car will not be able to reach town C are as follows Case 1: H1 and H2 closed…

Q: a) Prove the De Morgan's rule for events A and B using Venn diagram

A:

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: Let P(A) and P(B) be the probabilities that events A and B will occur. Which of the following is…

A: Solution

Q: Let V be the event that a computer contains a virus, and let W be the event that a computer contains…

A: Given that; P(V)=0.48P(W)=0.20P(V and W)=0.17

Q: Let V be the event that a computer contains a virus, and let W be the event that a computer contains…

A:

Q: In any given turn while playing a board game, the probability that a player will win a second turn…

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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: The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during…

A: Let X be the random variable having probability mass function is,  X 0 1 2 3 4 5 P(X=x)  0.03…

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 ∪…