동전 던지기 확률 보기

ㄱ. 동전을 $10$회 던질 때, 앞면이 $k$회 나타날 확률을 $P _{k}$라 하면 $\displaystyle P _{4} = _{10} C _{4} \left( \frac{1}{2} \right) ^{4} \left( \frac{1}{2} \right) ^{6}$$\displaystyle = _{10} C _{4} \left( \frac{1}{2} \right) ^{10}$ $\displaystyle P _{6} = _{10} C _{4} \left( \frac{1}{2} \right) ^{6} \left( \frac{1}{2} \right) ^{4}$$\displaystyle = _{10} C _{4} \left( \frac{1}{2} \right) ^{10}$ 그런데 ${}_{10} C _{4} = _{10} C _{6}$이므로 $P _{4} = P _{6}$ <참> ㄴ. $\displaystyle P _{5} = _{10} C _{5} \left( \frac{1}{2} \right) ^{5} \left( \frac{1}{2} \right) ^{5}$$\displaystyle = _{10} C _{5} \left( \frac{1}{2} \right) ^{10}$ 동전을 $20$회 던질 때, 앞면이 $10$회 나타날 확률을 $Q _{10}$이라 하면 $\displaystyle Q _{10} = _{20} C _{10} \left( \frac{1}{2} \right) ^{10} \left( \frac{1}{2} \right) ^{10}$$\displaystyle = _{20} C _{10} \left( \frac{1}{2} \right) ^{20}$ $\therefore P _{5} \ne Q _{10}$ <거짓> ㄷ. $P _{0} + P _{1} + P _{2} + P _{3} + P _{4} + P _{5}$ $\displaystyle = _{10} C _{0} \left( \frac{1}{2} \right) ^{10} + _{10} C _{1} \left( \frac{1}{2} \right) ^{10} + _{10} C _{2} \left( \frac{1}{2} \right) ^{10} + _{10} C _{3} \left( \frac{1}{2} \right) ^{10}$ $\displaystyle + _{10} C _{4} \left( \frac{1}{2} \right) ^{10} + _{10} C _{5} \left( \frac{1}{2} \right) ^{10}$ $\displaystyle = ( 1 + 10 + 45 + 120 + 210 + 252 ) \left( \frac{1}{2} \right) ^{10}$$\displaystyle = \frac{638}{1024}$$> 0.5$ <참>