Please be patient with my English, as I am a native Korean and English is not my first language.

I want to write a story about a political organization built on fortune-telling.

Let us assume there are fortune-tellers who accurately predict the future more than 50% of the time, without any prior or inside information.

And, at this time, 'the probability' is not the probability of the fortuneteller's 'right foretell' but the probability that fortune-tellers present 'a right foretell'. [Edit: this sentence left as written.]

Here is my question.

If there is two fortune-tellers who have 60% chance of accurately answering a question about the future, is there a way to employ such fortune-tellers to increase the odds above 60%.

Would increasing the number of fortune-tellers to ten or more raise the odds of always making "right decisions?"

If possible, to optimize probability of accuracy, how should fortune-tellers foretell? [Edit: open-endedness of original preserved.]

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please... Now I'm in the envoronment that cannot use my language... english is terribly difficult. though this, i had to write this question to solve my terrible this question.. please give me a answer... T.T – user36187 Jul 20 '12 at 11:44
So, the question is: given that any fortune-teller's probability in predicting the outcome of an event (of binary type) is about 60%, how many fortune-tellers should a political organization hire to make the right choices? Is that right? – Raskolnikov Jul 20 '12 at 11:48
Yup! your think is right. – user36187 Jul 20 '12 at 11:53
daniell// I'm sorry. I really didn't know where to go to solve my question... :( – user36187 Jul 20 '12 at 11:55
My bad. I think Raskolnikov has interpreted your question correctly. – daniel Jul 20 '12 at 12:08

Here is how I understand your question: suppose the politician have to take a decision, having to choose between 2 possibilities. They ask the fortune tellers: "which decision should we take, A or B ?"

Now, the hypothesis are that the fortune tellers are correct with probability 60%, and that their answer are independant from what the other fortune tellers say.

If 1 fortune teller gives an answer: the probability to be correct is 60%

If 2 fortune tellers give an answer:

• it is possible neither is correct (probability of this happening is 16%),
• it is possible one of them is correct (probability is 48%),
• it is possible both are correct (p = 36%).

Is it what you want to know?

In general, if there are $n$ fortune tellers and you want to know the probability that $k$ of them are correct provided each of them has probability $p$ of being correct, the formula is:

$${n \choose k}p^k(1-p)^{n-k}$$