Solve this Bayesian problem. Jake has been arrested for petty larceny and his pa

Question

Solve this Bayesian problem. Jake has been arrested for petty larceny and his parole officer suspects that it's to pay for his drug problem. He knows that about 3% of the population as cocaine or prescription painkiller dependency. Of those, an estimated 45% regularly steal to support their habit. Among those who do not have dependency, only about 1% have committed theft in the past 5 years. Given that Jake has been arrested, what are the chances he is using drugs? A general Bayesian equation: H = hypothesis, D = Data P(H|D) = P(D|H) times P(H)/P(D|H) times P(H) + P(D|NOTH) times P(NOTH)

Explanation / Answer

probabilty of Jack being arrested for theft =0.03*0.45+0.97*0.01 =0.0232

hence chances of using drugs, given arrested =0.03*0.45/0.0232=0.581897

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