Question

Q-7. Depression is a mood disorder which is usually associated with significant mental health problems. In Canada, it is estimated that in the population of age 15 to 64, 16% of women and 8% of men suffer from depression. The ratio between the male and female populations for the Canadian adults aged 15 to 64 is 0.83. (a) What percentage of the Canadian population aged 15 to 64 consists of female? (b) What is the probability that a randomly chosen person of age 15 to 64 suffers from depression? (c) Is depression independent of gender? (d) What is the probability that a randomly chosen person of age 15 to 64 is a female, given that the person suffers from depression?

Answer 1

solution 2 Ratio between the male and the female population for the Canadiau adults aged is to su is 0.83 mal sol female =0.83 Also, male & female = a1 » 0.83 female & female = 1 female = 2.83 a 0.55 b) Using total probability we have P (Dep) = P (Dep (female) +P /eep | Make) P(real) – 0-16 (0.5s) to .08(ous) = 0.124 of No depresion is not independent of gender as we given.

d) Using Bayes theorem we have probability that a randomly choosen person is female, given that the person suffey from depression is P(Remale Dep) = Ploep/female) (female) P(Đen) = 0.16(o.55) o. 124 - 0.7L