Question

In: Statistics and Probability

Four witnesses, Alice, Bob, Carol, and Dave, at a trial each tell the truth with probability...

Four witnesses, Alice, Bob, Carol, and Dave, at a trial each tell the truth with probability 1/3 independent of each other. In their testimonies, Alice claimed that Bob denied that Carol declared that Dave lied. What is the conditional probability that Dave told the truth?

Expert Solution

Answer:-

Given that:-

Four witnesses, Alice, Bob, Carol, and Dave, at a trial each tell the truth with probability 1/3 independent of each other. In their testimonies, Alice claimed that Bob denied that Carol declared that Dave lied.

What is the conditional probability that Dave told the truth?

Writing Alice, if Alice tells truth or Alice^{c} if Alice. tells lie.

The only outcomes that are consistent with Dave telling the truth are

with a total probability of Likewise, the only outcomes that are consistent with Dave lying are

with a total probability of Writing S for the given Statement.

The conditional probability that Dave told the truth is 0.3170

orchestra answered 1 year ago

Both Alice and Bob toss a fair coin three times. The probability that Alice records a...

Both Alice and Bob toss a fair coin three times. The probability that Alice records a different numbers of heads than Bob is given by A/B, where A and B are relatively prime integers (greatest common divisor is 1). Find A + B.

Suppose Alice flips 4 coins and Bob flips 4 coins. Find the probability that Alice and...

Suppose Alice flips 4 coins and Bob flips 4 coins. Find the probability that Alice and Bob get the exact same number of heads.

Alice solves every puzzle with probability 0.6, and Bob, with probability 0.5. They are given 7...

Alice solves every puzzle with probability 0.6, and Bob, with probability 0.5. They are given 7 puzzles and each chooses 5 out of the 7 puzzles randomly and solves them independently. A puzzle is considered solved if at least one of them solves it. What is the probability that all the 7 puzzles happen to be solved by at least one of them?

At 9/1/2021 the capital balances are Alice 88870 Bob 68327 Carol 36294 David joins the partnership...

At 9/1/2021 the capital balances are Alice 88870 Bob 68327 Carol 36294 David joins the partnership by contributing $28687 for 10% of the capital. Under the bonus method, how much capital does Alice gain as a bonus? Answer: 2911 Under the goodwill method, what is Bob's capital position after David joins?

:) Alice and Bob play the following game: in each round, Alice first rolls a single...

:) Alice and Bob play the following game: in each round, Alice first rolls a single standard fair die. Bob then rolls a single standard fair die. If the difference between Bob’s roll and Alice's roll is at most one, Bob wins the round. Otherwise, Alice wins the round. (a) (5 points) What is the probability that Bob wins a single round? (b) (7 points) Alice and Bob play until one of them wins three rounds. The first player to...

Alice and Bob are playing a game in which each of them has three strategies, A,...

Alice and Bob are playing a game in which each of them has three strategies, A, B, or C. If their choices do not match (e.g., if Alice picks B and Bob picks C), then no money is exchanged; otherwise Alice pays Bob $6 (if they both choose A), or $3 (if they both choose B), or $1 (if they both choose C). Is this a zero-sum game? Find a mixed-strategy Nash equilibrium for it. Is this the only equilibrium...

Alice and Bob bet 50 dollars with each other in a game in which their friend...

Alice and Bob bet 50 dollars with each other in a game in which their friend Charlie tosses a two-sided coin 3 times in a remote location. If Alice correctly predicts the majority face (i.e. the face which occurred the most often in the three tosses), she gets to keep Bob's money as well. Charlie calls them and lets them know that at least 1 heads has occurred.a) Assuming that the coin was fair, what is the probability that the...

Anne, bob, and carol- all biostatisticians and epidemiologists- are emailing each other about plans for the...

Anne, bob, and carol- all biostatisticians and epidemiologists- are emailing each other about plans for the weekend. Anne suggests that they all go surfing to Santa Cruz, but bob writes back indicating that he is reluctant to do so because he is terrified of sharks. Carol responds by arguing that P(great weekend | surfing) is 0.80 and P(great weekend | no surfing) is 0.50. Assuming that Carol’s probabilities are correct, further assume for this example that each person’s weekend happiness...

Alice and Bob are have several piles of chips. On each turn they can either remove...

Alice and Bob are have several piles of chips. On each turn they can either remove 1 or 2 chips from one pile, or split a pile into two nonempty piles. Players take turns and a player that cannot make a move loses. Find the value of the Sprague–Grundy function for positions with one pile made of n chips. (Please do not forget to prove correctness of your asnwer.)

Explain the four truth tests and illustrate each with an example of a belief that would...

Explain the four truth tests and illustrate each with an example of a belief that would be true by its standard. Explain specific theories