Question

A man takes a step forward with a probability 0.4 and backwards with probability 0.6.Find the prob that at the end of 11 steps he is just 1 step away from the starting point?

Answer 1

I know there will be 2 cases..
Case 1: He takes 6 steps forward and 5 steps backward
Case 2: He takes 5 steps backward and 6 steps forward.
I also know it is based on Bernoulli Trials,but i don't know how to put it mathematically.

Answer 2

\[P(6\ of\ 11\ steps\ are\ forward)=\left(\begin{matrix}11 \\ 6\end{matrix}\right)\times0.4^{6}\times0.6^{5}\ .........(1)\]
\[P(5\ of\ 11\ steps\ are\ forward)=\left(\begin{matrix}11 \\ 5\end{matrix}\right)\times0.4^{5}\times0.6^{6}\ .........(2)\]
The values of probability calculated from equations (1) and (2) are added to find the required probability.

Answer 3

you are taking forward as sucess?
I mean how do u decide what is sucess and fail here

Answer 4

For the man to finish one step away from the starting point after 11 steps means that there are two events that are a success:
1. The man takes a total of 6 steps forward and 5 steps backwards, resulting in him finishing one step in front of his starting point.
2. The man takes a total of 5 steps forward and 6 steps backwards, resulting in him finishing one step behind his starting point.
The calculations that I have posted use the binomial distribution to find the values of probability for event 1 and event 2.