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Computer Science Level pending

Suppose you were to flip an unbiased coin 20 times. Consider the probability of seeing at least one occurrence of the pattern consisting of one head immediately followed by one tail immediately followed by one head immediately followed by either a head or a tail immediately followed by zero or more heads. If this probability is expressed as a fraction in lowest terms then what is the sum of the fraction's numerator and denominator.


The answer is 993171.

Bill Bell by Bill Bell , 74, Canada

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1 solution

Bill Bell
Oct 17, 2015 
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from itertools import product,repeat
from re import compile
from fractions import Fraction

N=20
patt=compile('HTH[HT]H*')

coin=['H','T']

count=0
total=0
for toss in product(*repeat(coin,N)):
    total+=1
    result=''.join(toss)
    m=patt.search(result)
    if m:
        count+=1
print N
print count, total, Fraction(count,total)
print Fraction(count,total).numerator+Fraction(count,total).denominator

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