Question

A most unusual Irish pub serves only Guinness and Harp. The owner of this pub observes that 85%of his male customers drink Guinness as opposed to 35% of his female customers. On any given evening, this pub owner notes that there are three times as many males as females. What is the probability that the person sitting beside the fireplace drinking Guinness is female?

Answer 1

Answer 2

SOLUTION :

P(Female) = 1/(1 + 3) = 1/4 = 0.25

P(Male)= 1 - 1/4 = 3/4 = 0.75

P(Guinness | Female) = 35% = 0.35 

P(Guinness | Male) = 0/85 

P(Guinness) 

= P(Guinness and Female) + P(Guinness and Male)

= P(Guinness | Female) * P(Female)  + P(Guinness | Male) * P(Male)

= 0.35*0.25 + 0.85*0.75

= 0.725 

P(Female | Guinness) 

= P(Female and Guinness) / P(Guinness)

= P(Female) * P(Guinness | Female) / P(Guinness)

= 0.25 * 0.35 / 0.725

= 0.1207 (ANSWER)