If A and C are two events in a probability model such that 0 < P(C)<1 and IP(A|C) < P(A), then necessarily P(A| CC) > P(A).

Q: prove that if an event A is independent, then its probability is either 0 or 1

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Q: If rain falls randomly with a 20% chance of rain on any given day, what is the probability that we…

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Q: A drag racer has two parachutes, a main and a backup, that are designed to bring the vehicle to a…

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Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: For independent events, the probability of happening of events simultaneously can be given the…

Q: First define any three events A,B,C in your daily life problems and prove addition law of…

A: Suppose me and my sister are alone in the home. We are feeling boring. Therefore, my sister…

Q: If E and F are events in a probability space with IP(E) + 0, P(F) 7 0, and P(E|F) = P(F|E) then E…

A: We want to tell you above statement is true or false

Q: If E, F, and G are events in a probability space and P(E) > P(F) and P(G) 7 0 then P(E\G) > P(F|G).

A: Conditional probability means probability of one event that depends on another event.  If A and B…

Q: If E and F are events in a probability space with P(E) + 0, P(F)+ 0, and P(EF) = P(F|E) then E and F…

A: The given statement is false here. We find a counter example to prove that statement is false here.

Q: Suppose that events E and F are independent, P(E) = 0.3, and P(F) = 0.7. What is the P(E and F)? The…

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Q: A stockbroker believes that under present economic conditions, a customer will invest in tax-free…

A: Define the following events:   A: a person invest in tax free B: a person invest in mutual fund

Q: In any given turn while playing a board game, the probability that a player will land on a blue…

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Q: If A is the complementary event of A, P(A ) = 1 – P(A)< 1.

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Q: In a large hospital, suppose that 35% of patients suffer from disease A, 40% of patients suffer from…

A: Disclaimer: Since you have posted a question with multiple subparts, we will solve first 3 subparts…

Q: If E and F are independent events with P(E) = 0.33 and P(F) = 0.33, then what is P(EC U U F)?

A: If E and F are independent events, then P(Ec∩F) = P(Ec)*P(F), where P(Ec) =[1 - P(E)] P(Ec∪F) =…

Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: Probability is a branch of mathematics or statistics that is basically deals with the probability of…

Q: If an event is certain, then its probability is 0. O True O False

A: Solution Answer is  False

Q: If A and B are two independent events such that P(AUB) = 0.8, and P(A) 0.3, %3D then Find P(B)?

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Q: If the probability for one and only one event of A and B to happen is 0.3, P (A) = 0.2 and P (B) =…

A: Given: P(A)=0.2 P(B)=0.3  the probability for one and only one event of A and B to happen is 0.3

Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: Given Traffic light A Traffic light  B Traffic light C P ( A ) P ( B ) P ( C ) 0.6 0.4…

Q: d) Suppose Trevor must leave at or before 7:30 to be on time for work. If Trevor leaves as soon as…

A: HERE GIVEN  PMF  OF X X = no. of minute trevor takes to leave for work

Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: The given probability that he is stopped by each of the three traffic lights. The probabilities are…

Q: At a certain high school, 50% of the lents are enrolled in a Spanish class and o are enrolled in a…

A: Given that P(students are enrolled in a Spanish class)=0.50 P(students are enrolled in a French…

Q: Let E and F be independent events with P(E) = 0.2 and P(F) = 0.2. What is the probability that at…

A: Solution: From the given information, E and F are independent events, P(E) = 0.2 and P(F)= 0.2.

Q: A CLASS IN ADVANCED PHYSICS IS COMPRISED OF 10 JUNIORS, 30 SENIORS AND 10 GRADUATE STUDENTS. THE…

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Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: Multiplication rule for independent events:If two events A and B are independent then the…

Q: If two events A and B are not disjoint, then the probability of their union

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Q: If the probabilities that an automobile machine will service 3,4,5,6,7, or 8, or more cars on any…

A: Given Information: The following table represents the number of cars that automobile mechanic will…

Q: Show that for any three events A, B, and C, the probability that at least one of them occurs is P(A)…

A: Probability

Q: Consider the type of clothes dryer (gas or el (a) If the probability that at most one of t

A: GIven, a) P(at most one of these customers purchases an electric dryer)  = P(x≤1)  = 0.423 P( at…

Q: Let P(A)=0.4, P(B)=0.3, if A and B are mutually exclusive，what is the probability that exactly one…

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Q: (1) Suppose an influenza epidemic strikes a city. In 10% of families the mother has influenza; in…

A: Given that, a family with a mother, father, and two children. Let A₁ = {mother has influenza), A₂ =…

Q: A group of students is surveyed and 55% of the group is from Midland and 40% of the group like…

A: According to the provided data, the probabilities are;

Q: a) Show that for any three events A, B, and C, the probability that at least one of them occurs is…

A: Given  We need to prove that for three events A,B and C,the probability that atleast one of them…

Q: Theorem 3.9. For two events A and B, P (AnB) = P(A) .P (B IA), P(A) > 0 = P (B) . P(A \B), P(B) >0 }…

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Q: If A and B are any two events with P(A) = .3 and P(BIA) = .5, then the joint probability of A and B…

A: Solution-: Given: P(A)=0.3, P(B/A)=0.5  We want to find P(A and B)=?

Q: If the joint probability of neither of two events, A and B, occurring is 0.08, the probability of…

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Q: A city has two daily newspapers, A and B. A survey of 100 residents of the city shows that 35 people…

A: Given, A survey of 100 residents of the city shows that 35 people subscribe to A, 60 subscribe to B…

Q: If two events are independent, then the conditional probability of one event given the other event…

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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)&gt;0 and P(B)&gt;0 i.e. both have positive…

Q: If A, B, and C are mutually exclusive events with P(A) = 0.3, P(B) = 0.2, and P(C) = 0.4, determine…

A: Ans#   Given  A, B, and C are mutually exclusive events with P(A) = 0.3, P(B) = 0.2, and P(C) = 0.4…

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…

A: It is given that the, P(A) = P(B) = 0.3 and  P(C) =0.5 and since these 3 events are independent.

Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: From the above missing data is : P (A) , P(B) &amp; P(C) For the independent events , multiplication…

Q: Suppose that events E and F are independent, P(E) = 0.3, and P(F) = 0.9. What is the P(E and F)? The…

A: The union and intersection probabilities of two events A and B are related by the following formula:…

Q: Suppose that events E and F are independent, P(E)= 0.4, and P(F)=0.7. What is the P(E and F)? The…

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Q: A lottery has a grand prize of $2,000,000, 4 runner-up prizes of $125,000 each, 11 third-place…

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Q: If E and F are mutually exclusive events with P(E) = 0.11 and P(F) = 0.38, then the value of P(EUF)…

A: Given that P(E) = 0.11, P(F) = 0.38

Q: 1. Suppose that the events A, B are independent. (a) Using the Law of Total Probability, show that…

A: Result: If A and B are independent then P(A and B)=P(A)P(B)

Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: According to the given information, PA=0.8PB=0.1PC=0.4   The chances of getting stopped by any of…

Q: What is the probability that the employee is not late for work? Please write your answer in decimal…

A: Given data:     The probability that an employee stop by the traffic light A is: P(A)=0.8. The…

Q: A drag racer has two parachutes, a main and a backup, that are designed to bring the vehicle to a…

A: Consider an event A defines that main parachute deploys and event B defines that backup parachute…