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Say a gossip magazine editor is paying 2 sources to gather information about a particular celebrity. From his past experience the editor knows source# 1 is right 80% of time, and source# 2 is right 65% of the time.

Now, for a particular case, the editor wants to be sure at least 95%. Say the source #1, gives the editor some information piece x. What is the end probability in the following cases:

a. source# 2 also gives same information b. source# 2 gives a different information about same thing than what source#1 gave.

In both above cases, what is the probability of the info from source #1 being correct?

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What did you try? Where are you stuck? What similar problems can you solve? – Did May 4 '12 at 17:09

We are invited to assume independence, though that assumption is extremely dubious for this situation.

For the first problem, we want to find the probability that the rumor they pass on is true. It is easiest to compute first the probability that the rumor is false, that is, the probability that $1$ and $2$ are both wrong.

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