(a) 500 adults were asked whether they will get married in the next 3 years. Their responses are recorded in the table. Would marry in the next 3 years? Yes (Y) No (N) Male (M) 150 150 Female (F) 100 100 If one adult is selected at random from these 500 persons, find the probability that: (i) the response is "Yes"; [3 marks] (ii) the response is "Yes' given female; [3 marks] (iii) the response is 'No' and a male; [3 marks] (iv) the response is "Yes" or female. [3 marks] (V) Are the events 'Male' and "Yes' independent? Explain why or why not. [3 marks] (vi) Are the events 'Female' and 'No' mutually exclusive? Explain why or why not. [3 marks] (b) A school finds that 30% of the students are low achievers. The Headmaster is instructed to devise a revision module that will improve the situation. One hundred students are chosen at random and are given the revision module. 90% of high achievers pass the test and 20% of low achievers also pass. (i) Based on these results, if a student chosen at random, takes the module, and passes it, determine the probability that he or she is a high achiever. [10 marks] (ii) If the student fails the module, calculate the probability that he or she is a high achiever. [15 marks]