연속한 수 뽑기 확률

주어진 조건에 따라 확률을 구해 보면 $\displaystyle \mathrm{P} _{2} = \frac{10}{{}_{11} C _{2}} = \frac{2}{11}$ $\displaystyle \mathrm{P} _{3} = \frac{9}{{}_{11} C _{3}} = \frac{3}{55}$ $\displaystyle \mathrm{P} _{4} = \frac{8}{{}_{11} C _{4}} = \frac{4}{165}$ $\displaystyle \mathrm{P} _{5} = \frac{7}{{}_{11} C _{5}} = \frac{1}{66}$ $\displaystyle \mathrm{P} _{6} = \frac{6}{{}_{11} C _{6}} = \frac{1}{77}$ $\displaystyle \mathrm{P} _{7} = \frac{5}{{}_{11} C _{7}} = \frac{5}{{}_{11} C _{4}} = \frac{1}{66} = P _{5}$ $\displaystyle \mathrm{P} _{8} = \frac{4}{{}_{11} C _{8}} = \frac{4}{{}_{11} C _{3}} = P _{4}$ $\displaystyle \mathrm{P} _{9} = \frac{3}{{}_{11} C _{9}} = \frac{3}{{}_{11} C _{2}} = P _{3}$ $\displaystyle \mathrm{P} _{10} = \frac{2}{{}_{11} C _{10}} = \frac{2}{{}_{11} C _{1}} = P _{2}$ ∴ $P _{k} = P _{12 - k}$ 따라서, ㄱ, ㄴ은 참이지만 최솟값은 $\mathrm{P} _{6}$이므로 ㄷ은 옳지 않다.