Question

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

• A. $0.368$
• B. $0.147$
• C. $0.22$
• D. $0.073$

Answer 1

Answer: (A)

$0.368$

If the man is one step forward after $11$ steps, he has taken $6$ forward and $5$ backward steps .
If the man is one step backward after $11$ steps, he has taken $5$ forward and $6$ backward steps.
There are only two possibilities.
Let success: forward step and failure: backward step
$\Rightarrow p=0.4$ and $q=0.6$
$P$(one step away)=$P$($6$ successes)$+P$($5$ successes)
$\therefore P$(one step away)${=}^{11}{C}_6{\left(0.4\right)}^6{\left(0.6\right)}^5{+}^{11}{C}_5{\left(0.4\right)}^5{\left(0.6\right)}^6{=}^{11}{C}_6{\left(0.4\right)}^5{\left(0.6\right)}^5$