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?

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Expert Solution

Answer:-

Given that:-

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

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