(c) Four age groups (5059 years, 6069 years, 7079 years, and 80 years and over) are under study to assess the proportion of individuals suffering from chronic obstructive pulmonary disorder (COPD) in the population of adults aged 50 years and over in a particular region. In increasing age order, the four age groups 0 make up 41%, 41%, 7% and 11% of the study population respectively; 0 have associated (conditional) probabilities of developing COPD 0.05, 0.18, 0.25 and 0.33 respectively. (i) What is the probability that a person aged 50 years or over develops COPD ? 2 MARKS (ii) A health record is discovered recordin the fact that a erson suffered from COPD, but the a e of the g P 8 person is omitted from the record. Given the COPD diagnosis, what is the probability that the person is aged 80 years or over ? 2 MARKS (iii) Five people aged 50 years and over are selected from the fopulatmn If the development of COPD for each of the five people can be regarded as a collection 0 mutually independent events, What Is the probability that at most one of the five develops COPD. 7 2 MARKS