2 A school has 900 pupils. For a survey, Jan obtains a list of all the pupils, numbered 1 to 900 in alphabetical order. She then selects a sample by the following method. Two fair dice, one red and one green, are thrown, and the number in the list of the first pupil in the sample is determined by the following table.
| \cline { 3 - 8 }
\multicolumn{2}{c|}{} | Score on green dice |
| \cline { 3 - 8 }
\multicolumn{2}{c|}{} | 1 | 2 | 3 | 4 | 5 | 6 |
| 1,2 or 3 | 1 | 2 | 3 | 4 | 5 | 6 |
For example, if the scores on the red and green dice are 5 and 2 respectively, then the first member of the sample is the pupil numbered 8 in the list.
Starting with this first number, every 12th number on the list is then used, so that if the first pupil selected is numbered 8 , the others will be numbered \(20,32,44 , \ldots\).
- State the size of the sample.
- Explain briefly whether the following statements are true.
(a) Each pupil in the school has an equal probability of being in the sample.
(b) The pupils in the sample are selected independently of one another. - Give a reason why the number of the first pupil in the sample should not be obtained simply by adding together the scores on the two dice. Justify your answer.