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Quantitative Methods Q186

186ABC Juices Limited has outlets in the city as well as the suburbs. 60% of the people live in the city, while the rest live in the suburbs. ABC’s juices are consumed by 50% of the people in the city and 25% of those in the suburbs. The probability that a person chosen at random lives in the city given that he consumes ABC Juices is closest to:
  • Option : C
  • Explanation : First, note down the various probabilities given in the problem: P (City) = 0.60 P (Suburbs) = 0.40 P (Consumers | City) = 0.50 P (Consumers | Suburbs) = 0.25 P (City | Consumer) = [ P (Consumer | City) * P (City) ] / { [ P (Consumer | City) * P (City) ] + [ P (Consumer | Suburb) * P (Suburb) ] } P (City | Consumer) = ( 0.50 * 0.60 ) / [ ( 0.50 * 0.60) + ( 0.25 * 0.40 ) ] = 0.75
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