Bayes' Theorem: Suppose that E and F are two events from a sample space S such that p(E) 0 and p(F) #0. Then: Question: P(F\E)= P(EF)P(F) P(E\F)P(F)+P(EF)P(F) We have two boxes. The first box contains two green balls and seven red balls. The second contains four green balls and three red balls. Bob selects one of the boxes at random. Then he selects a ball from that box at random. If he has a red ball, what is the probability that he selected a ball from the first box. Let E be the event that Bob has chosen a red ball and F be the event that Bob has chosen the first box. The questions is: To find P(FIE) by using Bayes' theorem.

Q: Suppose A and B are events in a sample space with P(A) = 0.62, P(B) = 0.67, P(BU A) = 0.91 Find the…

A: Given A and B events of a sample space where; P(A)=0.62P(B)=0.67P(B∪A)=0.91 (a) We know by addition…

Q: A and B are two events such that P(A)-0.5 and P(B)-0.6 and P (AIB) = - then P (AIB) = 0.9 1 0.6 not…

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Q: Let A and B be two events of the same sample space. If P(A∖B)=0.3 and P(A∩B)=0.4 then: P(A)=

A: From the provided information, P (A\B) = 0.3 and P (A Ո B) = 0.4

Q: Two events A and B are independent if... There are 3 different formulas to test for probability…

A: We have given thatTwo events A and B are independent

Q: Let A, B be events with P(A) = .60,  P(B) = .20, and P(A and B) = .10.  Find P(A|B)

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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: Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.6, and P(A  B) = 0.15.…

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Q: Events A1, A2 and A3 form a partiton of the sample space S with probabilities P(A1) = 0.3, P(A2) =…

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Q: An experiment consists of two trials. The outcomes of independent the first trial are A, B, and C,…

A: Given information: An experiment consists of two independent trials. The outcomes of the first trial…

Q: A sample space consists of five simple events with P(E₁) = P(E₂) = 0.2, P(E) = 0.45, and P(EA) =…

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Q: An educator wants to construct a 98% confidence interval for the proportion of elementary…

A: As per our guidelines we are suppose to answer only one question kindly post the remaining questions…

Q: Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.5, and P(A N B) = 0.24.…

A: a) We are going to use the conditional probability formula and plug the given values in it

Q: Events A1, Az and A3 form a partiton of the sample space S with probabilities P(A¡) = 0.2, P(A2) =…

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Q: (A) (B) (C) Brand A Brand B Brand C (P) 5. Cup (E) 6 6 8. Cone Select all that apply. Which two…

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Q: Suppose that E and F are two events and that P(E) = 0.5 and P(F|E) = 0.2. What is P(E and F)? P(E…

A: GivenP(E)=0.5P(F|E)=0.2

Q: A grocery store employs cashiers, stock clerks, and deli/bakery workers. The distribution of…

A:

Q: (a)You enter a tournament where there are only three types of players (excellent, good and regular).…

A: We have to find the probabilities using classical theorem of probability.

Q: Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.5, and P(A ∩ B) = 0.18.…

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Q: Suppose that E and F are two events and that P(E) = 0.3 and P(F|E) = 0.6. What is P(E and F)? P(E…

A: We have to find p( E and F)

Q: Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.5, and P(A ∩ B) = 0.21.…

A: Given: P(A)=P(B)=0.5  And P(A∩B)=0.21 We know that P(A|B) = P(A∩B)/P(B) And P(B|A) = P(A∩B)/P(A).

Q: Events A and B are defined on a sample space S such that P {(A ∪ B)c} = 0.5 and P(A∩B) = 0.2. What…

A: P((A∪B)c)=0.5 P(A∩B)=0.2

Q: Suppose P(A) = 0.28 and P(B) = 0.48 and A and B are independent. Events A and B are not disjoint.…

A: Answer is mentioned below

Q: If P(A) = 0.4, P(B) = 0.2, and P(AU B) = 0.6, then P(AN B) = (a) Are events A and B independent?…

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Q: Suppose that E and F are two events and that P(E)= 0.8 and P(F|E) = 0.3. What is P(E and F)? .....…

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Q: If P(A) = 0.2, P(B) = 0.3, and P(A U B) = 0.48, then P(An B) =|. (a) Are events A and B independent?…

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Q: Suppose you roll two dice. Let X represent the number of even numbers appearing on the dice. For…

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

A: Given :

Q: A: A box contains (3) red balls, (6) White balls ,and (9) blue balls, we draw two balls with return,…

A: Given a box contains 3 red balls, 6 white balls and 9 blue balls, draw two balls with return from…

Q: Given P(A and B) = 0.43, P(A) = 0.81, and P(B) = 0.25 are events A and B independent or dependent?…

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Q: (III) A bowl contains many red, orange, and green jelly beans,in equal numbers. You are to make a…

A: (a) Sl No Macro states Macro states Microstates 1 3 green, 0 Orange & 0 Red GGG - - 1 2 2…

Q: A coin is tossed two times; let H represent a "head" and T for "tail" outcome (a) Define the sample…

A: We have given that A coin is tossed two times; let H represent a "head" and T for "tail" outcome…

Q: A grocery store employs cashiers, stock clerks, and deli/bakery workers. The distribution of…

A: The given contingency table is Dependents Cashiers Stock Clerks Deli/Bakery Workers Total…

Q: Let a&b be events with p(a)=0.2,p(b)=0.8, & p(b/a)=0.3. Find p(a&b)

A: Given Information: A and B are two events. P(A) = 0.2, P(B) = 0.8, P(B|A) = 0.3 To find the…

Q: A and B are both events in sample space S.   P(A)=0.4 P(B)=0.3 P(A and B) =0.2   What's the…

A: A and B are both events in sample space S. Given, P(A)=0.4 P(B)=0.3 P(A and B) =0.2

Q: Suppose P(A) = .70, P(B) = .18, and events A and B are mutally exclusive. Find:  a) P(A and B) b)…

A: The provided information are :P(A) = 0.70, P(B) = 0.18The events A and B are mutually exclusive.

Q: Given P(A and B) = 0.43, P(A) = 0.81, and P(B) = 0.25 are events A and B independent or dependent?

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Q: Let A and B be events with P(A) = 0.8; P(B) = 0.4, and P(B|A) = 0.2. Find P(A and B). O 0.16 O 0.25…

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Q: Let A and B be two events in a sample space S such that P(A) = 0.6, P(B) = 0.4, and P(A ∩ B) = 0.3.…

A: According to the given information in this question We need to find the following probabilities

Q: Let A and B be events with P(A) =0.4, P(B) =0.7, and P(B|A) =0.5. Find P (A and B).

A: The question is about prob. of events Introduction : If A and B are two events then the condition…