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A man lost in the woods decides to flip a coin, walking one mile east each time it appears heads and one mile west each time it appears tails.  He flips the coin six times and walks accordingly.  Find the probability that he will be at least two miles from his starting point at the end of this procedure.

 Dec 31, 2019
 #1
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There  are   2^6  =   64 possibilites

 

He will be less than  two milles from his starting point only when  3 heads  and 3 tails  occur  in any sequence of 6 flips

 

So......  

 

TTTTTT  =    1  way

TTTTTH  =    6 ways

TTTTHH  =  choose  tails to occur in any four of six positions  =     C(6,4)  = 15 ways

HHHHHH  = 1 way

HHHHHT  =  6 ways

HHHHTT = choose heads to occur  in any four of six positions  C(6, 4)  =  15 ways

 

So......the probability =

 

2 [  1 +  6   + 15 ]               22               11

______________   =        ___  =        ___ 

           64                           32               16

 

 

cool cool cool

 Dec 31, 2019

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