Please help with these 2 questions, give all work:

1)

The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group-blood group combinations. Blood Group 0 A B AB 1 0.082 0.102 0.011 0.004 Ethnic Group 2 0.139 0.141 0.018 0.003 3 0.215 0.194 0.071 0.020 Suppose that an individual is randomly selected from the population, and dene evens by A = {type A selected}, 3 = {type B selected}, and C = {ethnic group 3 selected}. (a) Calculate PM), P(C), and PM n C). (Enter your answers to three decimal places.) m = E m = S me) = E (b) Calculate both P(A|C) and F(C|A). (Round your answers to three decimal places.) me) = S W) = E Explain in context what each of these probabilities represents. (Select all that apply.) D If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A|C). Cl If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C|A). D If we know that the individual came from ethnic group 3, the probability that he has type A blood is given by P(A|C). Cl If a person has type A blood, the probability that he is from ethnic group 3 is given by P(C|A). [3 If a person has type B blood, the probability that he is from ethnic group 3 is given by P(A|C). Cl If we know that the individual came from ethnic group 3, the probability that he has type A blood is given by P(C|A). (c) If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1? (Round your answer to three decimal places.) Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects. (a) How many ways are there to randomly select 7 of these keyboards for a thorough inspection (without regard to order)? 480700 I ways (b) In how many ways can a sample of 7 keyboards be selected so that exactly two have an electrical defect? Ex (c) If a sample of 7 keyboards is randomly selected, what is the probability that at least 6 of these will have a mechanical defect? (Round your answer to four decimal places.) :lx