Question

Researchers propose a relationship between a person’s height and resistance to a particular disease. It was found that 20% of shorter people were resistant while the corresponding percentage for tall people was 35%. Of the people tested, 60% were tall.
(i) Produce a contingency table.
(ii) Suppose that a person is resistant to the disease, what is the probability that they are tall?
(iii) Suppose that a person is chosen at random, what is the probability that it is not resistant to the disease?
(iv) How likely is it that a randomly selected person is tall and not resistant to the disease?

Answer 1

Soli Tall people = 0.60 0.40 Given that 60%. se Shorter' people 40% • 204 0f shorter people resistant disease 20 X 0.40 de 0.08 = 1oo and 35% of tall people resistant disease 35 x0.60 100 0.21 10) Now. We construct the contingency table.. Tall short Resistant disease 0.21 0.08 Not Resist. dis 0.60 -0.21=0.39 0.40 -0.08=032 Total 0.60 0.40 Total 0.29 0.71 (6) Poob of tall, given that he is resist to disease Prob. of tall & resist. dise Prob- of fessist to diseases 0.21 0.29 0.7241 An (c) to Prob. that a person is not resistant the disease 0.71 An Bob that a person is tall and not resistant to the disease = 0.39 As (2)