A) \[\frac{{{2}^{5}}{{.3}^{5}}}{{{5}^{10}}}\]
B) \[462\times {{\left( \frac{6}{25} \right)}^{5}}\]
C) \[231\times \frac{{{3}^{5}}}{{{5}^{10}}}\]
D) None of these
Correct Answer: B
Solution :
[b] 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 \[=q=0.6=\frac{3}{5}.\] 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 \[=\,{{\,}^{11}}{{C}_{6}}{{p}^{6}}{{q}^{5}}+\,{{\,}^{11}}{{C}_{5}}{{p}^{5}}{{q}^{6}}\] \[=\,{{\,}^{11}}{{C}_{6}}{{\left( \frac{2}{5} \right)}^{6}}.{{\left( \frac{3}{5} \right)}^{5}}+\,{{\,}^{11}}{{C}_{5}}{{\left( \frac{2}{5} \right)}^{5}}.{{\left( \frac{3}{5} \right)}^{6}}\] \[=462\times {{\left( \frac{6}{25} \right)}^{5}}\]
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