### prob.

Question Sample Titled 'prob.'

Blake owns a company. The following shows the salaries (in ) of the staff in his company.

${20000}$ ${18000}$ ${10000}$ ${26000}$ ${12000}$ ${12000}$ ${10000}$ ${9000}$ ${114000}$

 (a) Write down mean of the salaries correct to one decimal place. (1 mark) (b) Two staff are selected randomly. Find the probability of each of the following. (i) The salary of one staff is at least $14000$14000$ more than the other. (ii) Both of them have the same salary. (iii) One of them has salary lower than the mean while the other has salary higher than the mean.  (6 marks) (c) When asked for a salary increase, Blake rejected by pointing out that the mean of the salaires is slightly higher than that of other companies of the same industry. Give one reason that Blake has applied the measure of central tendency inappropriately. (1 mark) 題解  (a) ${25667}.$ 1A (b) Sort the data in asc. order: ${9000}$ ${10000}$ ${10000}$ ${12000}$ ${12000}$ ${18000}$ ${20000}$ ${26000}$ ${114000}$ Number of possible outcomes$={{C}_{{2}}^{{9}}}={36}$ (bi) By counting, there are ${11}$ favourable outcomes. 1A $\therefore$Required prob.$=\dfrac{{11}}{{36}}$ 1A (bii) By counting, there are ${2}$ favourable outcomes. 1A $\therefore$Required prob.$=\dfrac{{2}}{{36}}=\dfrac{{1}}{{18}}$ 1A (biii) By counting, there are ${14}$ favourable outcomes. 1A $\therefore$Required prob.$=\dfrac{{14}}{{36}}=\dfrac{{7}}{{18}}$ 1A (c) Since there is an extreme value$114000$114000$ and there are only relatively small amount of data (${9}$ only), the mean value is not appropriate to represent the salaries of the majority. 1A

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