# The optimal questionnaire. You would like to participate in a TV game: you will have to find the…

The optimal questionnaire.

You would like to participate in a TV game: you will have to find the profession of a person (“chosen at random”) by three yes or no questions. You look at the statistics: there are 16 main professions P1, P2, . . . , P 16, occurring with the following frequencies:

p(P1) = 0.40, p(P5) = 0.05, p(P9) = 0.02, p(P13) = 0.01,

p(P2) = 0.18, p(P6) = 0.04, p(P10) = 0.02, p(P14) = 0.01,

p(P3) = 0.10, p(P7) = 0.03, p(P11) = 0.02, p(P15) = 0.01,

p(P4) = 0.06, p(P8) = 0.03, p(P12) = 0.01, p(P16) = 0.01.

(a) Find the strategy for the optimal questionnaire.

(b) Will you have a good chance (with only three questions)?

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