If a company wants to survey the use of the new communication channel promoted a

Question

If a company wants to survey the use of the new communication channel promoted among female and male employees. Let's assume that 15% of all employees use this new communication channel. The company also has the conditional probabilities of the new communication channel adoption for females and males respectively. Given the following known opportunities, please calculate posterior opportunities for male user, male non-user, female user and female non-user....-- Given probabilities Prior probabilities Bayesian revision Unconditional probabilities of test results Male Femal User Non-user 0.15 0.85 0.548 0.452 Conditional probabilities of test results User Non-user 0.53 0.47 Posterior probabilities User Non-user Male Female 0.65 0.35 Male Female

Explanation / Answer

P( male | user) = P( user | male) * P( male) / P( user)

0.65 = P(user | male) * 0.548 / 0.15

P( user | male) = 0.177

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P( male | non-user) = P( non-user | male) * P( male) / P( non-user)

0.53 = P(non-user | male) * 0.548 / 0.85

P( user | male) = 0.822

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P( female | user) = P( user | female) * P( female) / P( user)

0.35 = P(user | female) * 0.452 / 0.15

P( user | male) = 0.116

...................................................................

P( female | non-user) = P( non-user | female) * P( female) / P( non-user)

0.47 = P(non-user | female) * 0.452 / 0.85

P( user | female) = 0.883

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