If a drunkard person tries to take a step, then it will be a forw… - Vidyadip

MCQ

If a drunkard person tries to take a step, then it will be a forward or backward step with probabilities $\frac{1}{4},\frac{1}{2}$ respectively, or he will remain in 'as it is' position. If he tries to take a step $5$ times, then probability that he will be one step away from the initial position

A
$\frac {210}{2^8}$
✓
$\frac {315}{2^{10}}$
C
$\frac {171}{2^{16}}$
D
$\frac {75}{2^8}$

✓

Answer

Correct option: B.

$\frac {315}{2^{10}}$

b
cases

$(i)$ $\quad 2$ steps forward, $3$ steps backward

$(ii)$ $3$ steps forward, $2$ steps backward

$(iii)$ $2$ steps 'as it is', $2$ steps forward, $1$ step back.

$(iv)$ $2$ steps as it is', $2$ steps back, $1$ step forward.

$(v)$ $4$ steps is it is', $1$ step back.

$(vi)$ $4$ steps 'as it is', $1$ step forward.

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