N1977 P1 Q12

A test consists of five multiple choice questions to each of which three answers are given, only one of which is correct. For each correct answer a candidate gets \(2\) marks, but loses \(1\) mark for each incorrect answer. A particular candidate answers all question purely by guesswork. Draw up a table to show all the possible total marks from \(-5\) to \(10\) and the probability associated with each mark for this candidate. Use the table to show that the expected mark is zero, and find the variance of this distribution.