Question

A man takes a step forward with the probability of $0.4$ and one step backward with the probability of $0.6$, then the probability that at the end of eleven step he is one step away from the starting point is

• A. ${}^{11}{C}_5\times (0.48{)}^5$
• B. ${}^{11}{C}_6\times (0.24{)}^5$
• C. ${}^{11}{C}_5\times (0.12{)}^5$
• D. ${}^{11}{C}_5\times (0.72{)}^6$

Answer 1

The correct option is B ${}^{11}{C}_6\times (0.24{)}^5$

$\because \text{He is one step away from the starting point}\therefore \text{The probability of last step is}1$
Now probability ${=}^{11}{C}_6{\left(0.4\right)}^5{\left(0.6\right)}^5{=}^{11}{C}_6{\left(0.24\right)}^5$