Question

In a certain population 20% are heavy smokers, 30% are light smokers, and 50% do not smoke at all. In addition, in this population the probability of having high blood pressure is 0.35. The probability of having low blood pressure given that a person does not smoke is 0.8. The probability of having low blood pressure given that the person is a light smoker is 0.75.

a) What is the probability of having high blood pressure given that a person is a heavy smoker?

b) A random person was selected from this population. What is the probability that he is not a smoker given that he has low blood pressure?

Answer 1

a)P(high blood pressure)=P(heavy smoker)*P(high blood pressure|heavy smoker)+P(light smoker)*P(high blood pressure|light smoker)+P(do not smoke)*P(high blood pressure|do not smoke)

0.35=0.2*P(high blood pressure|heavy smoker)+0.3*(1-0.75)+0.5*(1-0.8)

0.2*P(high blood pressure|heavy smoker)=0.35-(0.3*(1-0.75)+0.5*(1-0.8))

P(high blood pressure|heavy smoker)=0.165/0.2 =0.875

b)

P(not a smoker|low blood pressure)=P(not smoke and low blood pressure)/P( low blood pressure)

=0.5*0.8/(1-0.35)=0.615385