(1 point) In a large population the probability of someone being stricken with t

Question

(1 point) In a large population the probability of someone being stricken with the euphoric mental state "StatsOnMyMind-itis" is 0.105. The probability of a person with StatsOnMyMind-itis of getting into a stats-related conversation is 0.946. The probability of a person that doesn't have StatsOnMyMind-itis of getting into a stats-related conversation is 0.742 (a) What is the probability of having StatsOnMyMind-itis and ending up in a stats-related conversation? 0.09933 (b) What is the probability of having StatsOnMyMind-itis and not ending up in a stats-related conversation? 0.00567 (c) What is the probability of not having StatsOnMyMind-itis and ending up in a stats-related conversation?0.66409 (d) What is the probability of not having StatsOnMyMind-itis and not ending up in a stats-related conversation? 0.23091 (e) What is the probability of having StatsOnMyMind-itis given that you just ended up in a stats-related conversation? (f) What is the probability of not having StatsOnMyMind-itis given that you just ended up in a stats-related conversation? (g) What is the probability of having StatsOnMyMind-itis given that you have not ended up in a stats-related conversation? (h) What is the probability of not having StatsOnMyMind-itis given that you have not ended up in a stats-related conversation?

Explanation / Answer

Let M = having stats on my mind

M’ = not having stats on my mind

C= ending up in a stats related conversation

C’ = not ending up .....

P(M) = 0.105

P(M’) = 0.895

P(C|M) 0.946

P(C’| M) = 0.054

P( C|M’) = 0.742

P(C’|M’) = 0.258

(a) P ( C and M) = P ( C|M) . P( M) = 0.09933

(b) P ( C’ and M ) = 0.00567

(c) P ( C and M’ ) = 0.66409

(d) P ( C’ and M’ ) = 0.23091

(e) P( M | C) = P (C | M ) . P(M) / [P (C|M) . P(M) + P (C|M’) . P(M’) ] = 0.1301

Note: using Bayes’ theorem

(f) P ( M’|C) = P( C|M’) . P( M’) / [ P(C|M’). P(M’)+ P (C|M) . P(M) ] = 0.86989

(g) P ( M|C’) = P (C’|M) . P( M ) / [P ( C’|M) . P(M) + P(C’|M’). P(M’)]= 0.02397

Similarly

(h) P(M’|C’) = 0.97603

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