Three mechanics are trying to repair a machine. Each mechanic is capable with probability 0.4 and otherwise clueless; their capabilities are uncorrelated. The machine either has a small fault or is completely broken, each with probability 0.5

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Three mechanics are trying to repair a machine. Each mechanic is capable with probability 0.4 and

otherwise clueless; their capabilities are uncorrelated. The machine either has a small fault or is

completely broken, each with probability 0.5. In the first case, only a capable mechanic can repair it; in

the second case nobody can repair it. The mechanics don’t know the state of the machine before they

start working on it.

Assume that we don’t know the state of the machine or the ability of mechanic 1, but we know

that mechanic 1 was not able to repair the machine. What is our posterior belief that the machine

is completely broken (i.e. the probability with which we think the machine is broken after having

seen that mechanic 1 could not repair it)?

Now assume that we don’t know the state of the machine or the abilities of mechanics 1 or 2, but

we know that both 1 and 2 were not able to repair the machine. What is our posterior belief that

the machine is completely broken?

Now assume that there were many mechanics, all of whom are capable with probability 0.4. We

observe that one mechanic after the other tries to repair the machine and fails. Can we ever be

100% sure that the machine is broken? If yes, when? If not, why not?

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