The prevalence of diabetes mellitus in a population was found to be 10 per cent. What is the probability that three people selected at random from the population have the disease?

Three people randomly selected from a population and having diabetes are events occurring together but not associated with each other i.e. they are independent of each other. Hence, the multiplication law of probability is applicable here. Since the probability of one person having the disease is 10 per cent or 1/10, the probability of three people having the disease is 1/10 x 1/10 x 1/10 = 1/1000 or 0.001. Ref: Methods in Biostatistics: For Medical Students and Research Workers, By BK Mahajan, Sixth Edition, Pages 105-108.