# Answer these 3 geographic information systems questions

Week 6 Assignment Total: 25pts Note: You have to show how you arrived at these values to get full points. 1. Suppose that the proportions of blood phenotypes in a particular population are as listed in the following table. A B AB O 0.42 0.10 0.04 0.44 a) Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? (3pts) b) What is the probability that the phenotypes of two randomly selected individuals match? (3pts) c) What is the probability that the phenotype is A given that you already know that this individual is of type A, B, or AB but not O? (3pts) 2. The following table is for a population of 156 batteries, produced either by Machine A or Machine B. a) Suppose one of these 156 batteries is to be randomly selected. Let D be the event that the randomly selected battery is defective and let A be the event that the randomly selected battery is produced by Machine A. Calculate P(D) and P(D|A) (4pts) b) Are the events D and A independent? Justify your response using the definition of independent events. (3pts) 3. Suppose that in a population, 85% of the individuals drive to work and: ¡ Of those who drive to work, 78% live far from work. ¡ Of those who do not drive to work, 46% live far from work. An individual is to be randomly selected from this population. Let D be the event that the individual drives to work and let F be the event that the individual lives far from work. a) Compute the probability the randomly selected individual does not drive to work, ” ). (3pts) P(𝐷 b) Compute the probability the randomly selected individual lives far from work, P(F). (3pts) c) Compute the probability that the randomly selected individual drives to work, given he/she lives far from work, P(D|F). (3pts).