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A drunkard performs a brisk walk and takes a step forward with the probability of 0.3 followed by a step backwards and so on. What is the probability that at the end of 13th step he is one step away from the initial position

A drunkard performs a brisk walk and takes a step forward with the probability of 0.3 followed by a step backwards and so on. What is the probability that at the end of 13th step he is one step away from the initial position

Grade:12

2 Answers

Arun
25750 Points
6 years ago
Dear student
 
 
Hello student,
One step away means a step forward or a step backward
=> either he took 7 forward steps and 6 backward steps or 6
7backward steps and 6 forward steps
=> reqd. probability
= 13C7 * (0.3)^7 * (0.7)^6 + 13C6 * (0.3)^6 * (0.7)^7
 
 
Hope now you can solve tthi.
 
Regards
Arun (askIITians forum expert)
Archit
11 Points
6 years ago
hi Arun. I have a question. You assumed the probability of taking a step backwards = 1 – 0.3 = 0.7. This implies that you ignored the possibility that he doesn’t move at all. You assumed that 1 = P(forward step) + P(backward step). But ideally, it should be 1 = P(forward step) + P(backward step) + P(no step at all).

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