Answer Happy

2. (a) In the annual recruitment exercise of a large commercial company, all applicants are required to go through two tests which include a written test and an oral interview in the screening stage. The failure rates for the written test and the oral interview are 85% and 80% respectively, and 75% applicants fail both tests. Only those applicants who pass both tests in the screening stage will be invited for a final interview. Offers of employment are made to 25% of those invited for the final interview. i. Find the probability that a randomly selected applicant is invited for the final interview. [3 marks) ii. Find the probability that a randomly selected applicant passes the written test or passes the oral interview but is not invited for the final interview. [2 marks] iii. Find the probability that a randomly selected applicant passes the oral interview knowing that he/she has passed the written test. [2 marks] iv. Find the probability that only one of ten randomly selected applicants is offered employment. [3 marks] (b) There are three bags that each contains 100 marbles: • Bag 1 has 75 red and 25 blue marbles; Bag 2 has 60 red and 40 blue marbles; • Bag 3 has 45 red and 55 blue marbles. One of the bags is selected at random and then pick a marble from the selected bag, also at random. Suppose that the chosen marble is red. What is the probability that Bag 1 was selected? (5 marks (c) From an ordinary deck of playing cards, cards are drawn successively at random and without replacement. What is the probability that the third heart appears on the seventh draw? [5 marks)