7. Three prisoners are informed by their jailer that two of them have been chosen at random to be released. 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 that at least one of the two will go free. The jailer refuses to answer this question, pointing out that if A knew which of his fellow prisoners were to be set free, then his own probability of being released would decrease from 2/3 to 1/2 because he would then be one of the two prisoners who might be released. What do you think of the jailer's interpretation of probabilities?
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- 5. An office manager is looking to purchase a new printer for his office. He has narrowed his choices down to four printers but cannot decide which of the four he prefers. He has decided to choose two of the four printers at random, and then to let the other members of the office decide which of the two they prefer. The speeds, in pages per minute, of the four printers are 25, 30, 27, and 32. Considering the speeds of the two printers chosen to be the sample, what are the mean and the standard deviation of the sample mean?A poll released this week found that in a random sample of registered voters, 60% indicated that they think a fenmale "will run" for the presidency, 30% said a female “will not run," and 10% had “no opinion." When asked their opinions on whether or not a female could be elected, 66% of those who said a female "will run" thought a female could be elected; 25% of those who thought a female "will not run" thought a female could be elected; whereas, 20% of those who had no opinion said 4. that a female could be elected. а. [2] What percentage of registered voters (in this sample) thought that a female could be elected? [2] Given that a person thought that a female could be elected, what is the probability that this person said a female "will not run" for the presidency? b. [3] Given that a person thought that a female could be elected, which is more likely: that this person said a female “will not run" for the presidency or that this person said a female “will run" for the presidency? C.In a game show, a contestant is presented with three doors: Door A, Door B, and Door C. Behind one of these doors is a car, and behind the other two are goats. The contestant picks one door, say Door A, and the host, who knows what's behind each door, opens another door, say Door B, revealing a goat. The contestant is then given the choice to stick with their original choice (Door A) or switch to the remaining unopened door (Door C). What is the probability of winning the car if the contestant decides to switch doors?
- A penny is tossed three times and the results heads and tails noted. The process is continued until there are 100 sets of threes. In 69 cases, heads fell first, in 49 cases, heads fell second and in 53 cases. Heads fell third. In 33 cases heads fell both first and second and in 21 cases heads fell both second and third. Show that there must have been at least 5 occasions on which heads fell three times, and that there could not have been more than 15 occasions on which tails fell three times, though there need not have been any.The player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20. Give evidence that the player will theoretically win 20-40% of the timeSuppose 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.1)Bob Neverready has a portable TV. The TV uses two batteries and both of them are dead. Bob opens a new pack of four good batteries and dumps them on the table. Then he opens the TV and dumps the two dead batteries on the table with the good ones. The batteries get mixed up and Bob no longer knows which are which. (Has this ever happened to you?) If Bob picks two batteries off of the table at random and puts them into the TV, what is the probability that he chose two good batteries and that the TV will work? The average unemployment rate in California in August 2020 was 11.4%. 2)Assume that 550 employable people in California were selected randomly in August 2020. What is the expected value of the number of people in the sample who were unemployed? Round your answer to one decimal point 3)A deck of 52 playing cards consists of four suits, each with thirteen cards. In a certain card game, a hand consists of eleven cards selected randomly without replacement. What is the probability…The response already posted ons ite is not being accepted..Looking for a different outcome. Reeba randomly picks one of her 3 children to help her clean the house. She randomly assigns the child she picks to either clean the kitchen, living room or bedroom. Label her children O (Oldest), M (Middle) or Y (Youngest) and the job K (Kitchen), L (Living room) or B (Bedroom). [Use the order in which these are listed, abbreviate with captial letters, separate with commas, no spaces]
- Four salesmen play "odd man out" to see who pays for lunch. They each flip a coin, and if there is a salesman whose coin doesn't match the others he pays for lunch. To clarify, the "odd man" must get heads while the other three get tails OR he must get tails while the other three get heads. Of course, since it is possible for two men get heads and two men get tails, not all flips will result in finding an "odd man". If this occurs the salesmen would be forced to flip again. What is the probability that there is an "odd man" the first time they flip?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…