Other question about tourists.

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Can someone help me with this question ?

Mr Bayes goes to Bandrika. Tom is in the same position as you were in this problem:

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You are lost in the National Park of Bandrika. Tourists comprise two-thirds of the visitors to the park, and give a correct answer to request for directions with probability 3/4. (Answers to repeated questions are independent, even if the question and the person are the same). If you ask a Bandrikan for directions, the answer is always false.

(I) You ask a passer-by whether the exit from the park is East or West. The answer is East. What is the probability that is correct ?

(II) You ask the same person again, and receive the same reply. Show the probability that it is correct is 1/2.

(III) You ask the same person again, and receive the same reply. What is the probability that is correct ?

(IV) You ask for the fourth time, and receive the answer East. Show that the probability it is correct is 27/70.

(V) Show that, had the fourth answer been West instead, the probability that that East is nevertheless correct is 9/10.

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but he has reason to believe that, with probability P East is the correct answer. Show that:

(a) Whatever answer first received, Tom continues to believe that East is correct with probability P.

(b) If the first two replies are the same (that is, either WW or EE), Tom continues to believe that East is correct with probability P.

(c) After three like answer, Tom will calculate as follows, in the obvious notation:

P(East correct | EEE) = 9P/(11 - 2P)

P(East correct | WWW) = 11P/(9 + 2P)

Evaluate these when P = 9/20.
 

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