Question

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

• A. ${ } ^ { 11 } C _ { 6 } ( 0.24 ) ^ { 5 }$
• B. ${ } ^ { 11 } C _ { 6 } ( 0.4 ) ^ { 6 } ( 0.6 ) ^ { 5 }$
• C. ${ } ^ { 11 } C _ { 6 } ( 0.6 ) ^ { 6 } ( 0.4 ) ^ { 5 }$
• D. None of these

Answer 1

Answer: (A)

${ } ^ { 11 } C _ { 6 } ( 0.24 ) ^ { 5 }$

Answer 2

The man will be one step away from the starting point if (i) either he is one step ahead or (ii) one step behind the starting point.

∴ The required probability = P(i) + P(ii)

The man will be one step ahead at the end of eleven steps if he moves six step forward and five steps backward.

The probability of this event is ${ } ^ { 11 } C _ { 6 } ( 0.4 ) ^ { 6 } ( 0.6 ) ^ { 5 }$.

The man will be one step behind at the end of eleven steps if he moves six steps backward and five steps forward.

The probability of this event is ${ } ^ { 11 } C _ { 6 } ( 0.6 ) ^ { 6 } ( 0.4 ) ^ { 5 }$.

Hence the required probability

.