7. Three prisoners are informed by their jailer that two of them have been chosen at random to bereleased. Prisoner A asks the jailer to tell him privately which of his fellow prisoners will be set free,claiming that there would be no harm in divulging this information because he already knows thatat least one of the two will go free. The jailer refuses to answer this question, pointing out that ifA knew which of his fellow prisoners were to be set free, then his own probability of being releasedwould decrease from 2/3 to 1/2 because he would then be one of the two prisoners who might bereleased. What do you think of the jailer's interpretation of probabilities?

Answered: Image /qna-images/answer/0ae54c7e-b91e-4404-b415-a4152feff815.jpg

Answered: 7. Three prisoners are informed by…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An aesthetic club has 100 members. Out of them 40 do dancing, 45 do music and 24 do drama. 15 do both dancing and music, 11 do both dancing and drama and 13 do both music and drama and 5 do dancing, music and drama. Remaining members do arts. Let D represents the randomly selected member does dancing, M represents the randomly selected member does music, R represents the randomly selected member does drama. A represents the randomly selected member does arts. Represent the given information in a Venn diagram. Use that Venn diagram to answer the following questions. a) Find the probability that a randomly selected member either does dancing or music. b) Find whether the events “The randomly selected member does drama” and “The randomly selected member does music” are independent or not.
Show All Work Please... Consider a deck of cards that has 80 cards. Of these, 60 have a color and 20 are “wild.” The 60 cards with a color are either red, yellow, green, or blue, with 15 of each color. Two cards are said to “match” if any of the following are true: they have the same color, one is a color and the other is wild, or both are wild. (This is a simplified version of the card game UNO.) Two cards are drawn from the well-shuffled deck without replacement. Express your answers to (a)-(d) as simplified fractions or as percentages rounded to the nearest hundredth of a percent. (a) What is the chance that both are blue? _________ (b) What is the chance that both are color cards and they are the same color? _________ (c) What is the chance that one is a color card and the other is wild? _________ (d) What is the chance that they match, using the definition above? _________ (e) Are the following two events mutually…
In a survey of 1200 people, 80 indicated they were going to buy a new car, 70 said they were going to buy a new TV and 65 said they were going to buy a new stove. Of these, 30 were going to buy both a car and a TV, 35 were going to buy a car and a stove and 20 were going to buy a stove and a TV. Twenty people said they were going to buy all three items. A person is selected at random from this 1200 people . Given that this person was not going to buy a TV, what is the probability that he /she was not going to buy a car ?
A box contains r red balls and b blue balls. One ball is selected at random and its color is observed. The ball is then returned to the box and k additional balls of the same color are also put in the box. A second ball is then selected at random, Its color is observed & it's returned to the box together with k additional balls of the same color. Each time another ball is selected, the process is repeated. If four balls are selected, whats the probability that the first three balls will be red and the fourth be blue?
A product shipment contains 6 computer chips, of which two (2) are defective. If an inspector selects 4 chips at random for an order, without replacement, how many ways are there of picking both defective chips in this order (of 4 chips)? Order does not matter.
3. Suppose that a class contains 8 boys and 10 girls, and that 5 students are to be selected at random for a special assignment. The teacher wants at least one boy from the 5 students for this assignment. The number of ways are a. 8316 b. 42768 с. 11760 d. 997920
Suppose that we've decided to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While talking to her on the phone, we'll thoroughly shuffle a standard deck of 52cards (which is made up of 13 hearts, 13 spades, 13 diamonds, and 13 clubs) and draw one card at random. We'll ask Clara to name the suit (heart, spade, diamond, or club) of the card we drew. After getting her guess, we'll return the card to the deck, thoroughly shuffle the deck, draw another card, and get her guess for the suit of this second card. We'll repeat this process until we've drawn a total of 14 cards and gotten her suit guesses for each.Assume that Clara is not clairvoyant, that is, assume that she randomly guesses on each card. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution (that is, the expectation of…
Each of 27 tourists was asked which of the countries Angola (A), Burundi (B) and Cameroon (C) they had visited. Of the group, 15 had visited Angola, 8 had visited Burundi, 12 had visited Cameroon, 2 had visited all three countries, and 21 had visited only one. Of those who had visited Angola, 4 had visited only one other country. Of those who had not visited Angola, 5 had visited Burundi only. All of the tourists had visited at least one of these countries. (a) Draw a fully labelled Venn diagram to illustrate this information. (b) Find the number of tourists in set Bc and describe them. (C) Describe the tourists in set (A N B) UC c and state how many there are. (d) Find the probability that a randomly selected tourist from this group had visited at least two of these three countries.
6.) A mathematics class has 16 engineers majors, 12 science majors, and 4 liberal artsmajors.a.) What is the probability that a student selected at random will be a science orliberal arts major?b.) What is the probability that a student selected at random will be anengineering or science major?c.) 5 of the engineering students, 6 or the science majors, and 2 of the liberal artsmajors are female. What is the probability that a student selected at random is anengineering major or a female?
Suppose that we've decided to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While talking to her on the phone, we'll thoroughly shuffle a standard deck of 52 cards (which is made up of 13 hearts, 13 spades, 13 diamonds, and 13 clubs) and draw one card at random. We'll ask Clara to name the suit (heart, spade, diamond, or club) of the card we drew. After getting her guess, we'll return the card to the deck, thoroughly shuffle the deck, draw another card, and get her guess for the suit of this second card. We'll repeat this process until we've drawn a total of 14 cards and gotten her suit guesses for each. Assume that Clara is not clairvoyant, that is, assume that she randomly guesses on each card. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution (that is, the expectation of the relevant…
In a race with twelve horses, there are three prizes. Find the following: A. How many possibilities are there for the win, place, and show (first, second, and third) positions in a horse race with 12 horses if all orders of finish are possible? There are ? different ways. B. Suppose some nefarious individual lames three of the twelve horses ensuring that they won't be among the top finishers. How many possibilities are there for the win, place, and show (first, second, and third) positions in a horse race to happen now? There are ? different ways. C. Suppose the three top prizes are all equal in value assigned to the top three finishers. How many possibilities are there for the prizes in a horse race with 12 horses if all orders of finish are possible?
Three prisoners are informed by their jailer that one of them has been chosen at random to be executed, and the other two are to be freed. Prisoner A asks the jailer to tell him privately which of his fellow prisoners will be set free, claiming that there would be no harm in divulging this information, since he already knows that at least one will go free. The jailer refuses to answer this question, pointing out that if A knew which of his fellows were to be set free, then his own probability of being executed would rise from 1/3 to 1/2, since he would then be one of two prisoners. What do you think of the jailer's reasoning? 8.

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