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Question 2 (20 points) Q.2) Probability, Bayes' Theorem: 30% of the population in a country received complete vacci- nation against Covid19, 20% is partially vaccinated (received only the first dose of the vaccine), and 50% of the population has not received even the first dose. People are subject to regular Covid19 tests if they show some symptoms, even if they were completely vaccinated. The result of a positive test for a person from the completely vaccinated group is 5%, for a person from partially vaccinated group is 25%, and for a person from the unvaccinated group is 45%. Answer the following questions: (a) What is the probability that a randomly selected person from the population is partially vacci- nated? (b) What is the probability that a person with a positive test result is from the group that is partially vaccinated? (c) What is the probability that a person from the partially vaccinated group tests positive twice from two independent tests? (d) There is another test available which is more accurate for people who have not received any vaccination dose. The probability of a positive result for this test for a person from the completely vaccinated group is 15%, for a person from partially vaccinated group is 25%, and for a person from the third group is 35%. What is the probability that a person who tests positive for both tests (administered independently) belongs to the group completely vaccinated? (2+5+6+7 =20 marks