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A man takes a forward step with probability 0.8 and backward step with probability 0.2. What is the probability that at the end of 9 steps he is exactly three steps away from the starting point;

A man takes a forward step with probability 0.8 and backward step with probability 0.2. What is the probability that at the end of 9 steps he is exactly three steps away from the starting point; 

Grade:12th pass

1 Answers

Arun
25750 Points
4 years ago
One step away means a step forward or a step backward
=> either he took 6 forward steps and 5 backward steps or 6backward steps and 5 forward steps
=> reqd. probability
= 11C6 * (0.4)^6 * (0.5)^5 + 11C6 * (0.4)^5 * (0.6)^5
= 11C5 * (0.4)^5 * (0.6)^5 * (0.4 + 0.6) ... [11C6 = 11C5]
= (11x10x9x8x7)/(1x2x3x4x5) * (0.24)^5
= 0.368.
 
 

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