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Bayes Right-Winger Committee

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A Committee of three people has been formed by random selection from five left-wingers and four right wingers. The Committee members then vote for or against a strike whenever there is a dispute. Each left winger votes for a strike three out of four times in strike votes, whereas each right winger votes for a strike only once out of three times in strike votes. If it is known that the Committee has decided against one particular strike, what is the probability that there is a majority of right-wingers on the Committee?

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Solution Summary

The expert determines the probability that there is a majority of right-wingers on the committee.

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A be the event that committe has decided against one particular strike.
MLW be the event that majority are left wingers on committe.
MRW be the event that majortiy are right wingers on committe

P[ MRW / A ] = p[MRW] * p[ A/ MRW]
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p[MRW] * p[ A/ MRW] + p[MLW] * p[ A/ ...

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