Find the probability that a word with 15 letters (selected from P,T,I,N) does not contain TINT If a word with 15 letters is formed at random using the letters P, T, I, N,
find the probability that it does not contain the sequence TINT.
(I just made up this problem.)

The following Python script confirms the answer given by @McFry:
LENGTH = 15
LETTERS = 'PTIN'
SEQUENCE = 'TINT'

def func(word):
    if len(word) < LENGTH:
        return sum(func(word+letter) for letter in LETTERS)
    else:
        return SEQUENCE not in word

count = func('')
total = len(LETTERS)**LENGTH
print '{}/{}={}%'.format(count,total,100.0*count/total)

The output is $1024574807/1073741824\approx95.42\%$.
