Mathematics - Probability Question with Solution | TestHub

As $0.4+0.6=1$, the man either takes a step forward or a step backward. Let a step forward be a success and a step backward be a failure. Then, the probability of success in one step $=p=0.4=\frac{2}{5}$ The probability of failure in one step $=\mathrm{q}=0.6=\frac{3}{5}$ In 11 steps he will be one step away from the starting point if the numbers of successes and failures differ by 1 . So, the number of successes $=6$ The number of failures $=5$ or the number of successes $=5$, The number of failures $=6$ $\therefore$ the required probability $={}^{11}{\mathrm{C}}_6{\mathrm{p}}^6{\mathrm{q}}^5+{}^{11}{\mathrm{C}}_5{\mathrm{p}}^5{\mathrm{q}}^6$ $={}^{11}{\mathrm{C}}_6{\left(\frac{2}{5}\right)}^6\cdot {\left(\frac{3}{5}\right)}^5+{}^{11}{\mathrm{C}}_5{\left(\frac{2}{5}\right)}^5{\left(\frac{3}{5}\right)}^6$ $=\frac{11!}{6!5!}{\left(\frac{2}{5}\right)}^5\cdot {\left(\frac{3}{5}\right)}^5\left\{\frac{2}{5}+\frac{3}{5}\right\}$ $=\frac{\mathrm{11.10.9.8.7}}{120}\cdot \frac{2^5\cdot 3^5}{5^{10}}=462\times {\left(\frac{6}{25}\right)}^5$