7 On a multiple choice examination paper, each question has five alternative answers given, only one of which is correct. For each question, candidates gain 4 marks for a correct answer but lose 1 mark for an incorrect answer.
- James guesses the answer to each question.
- Copy and complete the following table for the probability distribution of \(X\), the number of marks obtained by James for each question.
| \(\boldsymbol { x }\) | 4 | - 1 |
| \(\mathbf { P } ( \boldsymbol { X } = \boldsymbol { x } )\) | | |
- Hence find \(\mathrm { E } ( X )\).
- Karen is able to eliminate two of the incorrect answers from the five alternative answers given for each question before guessing the answer from those remaining.
Given that the examination paper contains 24 questions, calculate Karen's expected total mark.