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You know that a certain letter is equally likely to be in any one of three different folders. Let αi be the probability that you will find your letter upon making a quick examination of folder i if the letter is, in fact, in folder i, i = 1, 2, 3. (We may have αi < 1.) Suppose you look in folder 1 and do not find the letter. What is the probability that the letter is in folder 1?

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P(F1)= Prob of letter in folder 1 = 1/3

P(F2)= PRob of letter in folder 2 =1/3

P(F3)= Prob of letter in folder 3 =1/3

P(not found in F1)= prob of letter not found in folder F1 = 1-a

P( present in F1)= Prob of letter  prsent in F1

question asked = P(letter present in F1 | letter not found in F1) = P(letter not found in F1 | letter present in F1) * P(letter present in F1) / P(letter not found in F1 | letter present in F1) * P(letter present in F1) + P(letter not found in F1 | letter present in F2) * P(letter present in F2) + P(letter not found in F1 | letter present in F3) * P(letter present in F3)

=>P(letter not found in F1 | letter present in F1) * P(letter present in F1) = (1-a) * 1/3

=> P(letter not found in F1 | letter present in F2) * P(letter present in F2) = 1 * 1/3 as if letter is present in F2 then prob of not finding it in F1 will be defnititly 1.

=> P(letter not found in F1 | letter present in F3) * P(letter present in F3) = 1 * 1/3

so,[(1-a) * 1/3] /[ (1-a) * 1/3 + 1/3 + 1/3] = 1-a / 3-a

please correct me
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