Question

Suppose a game piece is initially at the starting point of the board. We repeatedly flip a fair coin and the piece is moved one step left or right on the board depending on whether the coin shows heads or tails. Approximate the probability that after 400 flips the piece is no more than 10 steps away from the starting position. Assume the board is infiniteso you don’t need to worry about hitting the edge.

The answer of Probability equal to 0 is not correct.

Answer 1

Sample size , n =    400                              
Probability of an event of interest, p =   0.50                              
we need to calculate probability for ,                                  
195   ≤ X ≤    205                          
Mean = np =    200                              
std dev ,σ=√np(1-p)=   10.0000                              
                                  
P (   195   ≤ X ≤    205   )                  
Z1 =   (X1 - µ ) / σ =   -0.500                          
Z2 =   (X2- µ ) / σ =   0.500                          
                                  
P (    -0.5000   ≤ Z ≤   0.500   )                   
                                  
= P ( Z ≤   0.500   ) - P ( Z ≤   -0.500   ) =    0.6915   -    0.3085   =   0.3829

Thanks in advance!

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