What's bad in S

A biased coin having probability of tails appearing as \( \frac{2}{3} \) is tossed. If heads appears, 4 letters are chosen at random without replacement from the word CHRISTMAS, and if tails appears, 5 letters are chosen at random without replacement from the same word. Given that the chosen letters contain no S, the probability that tail appeared on the coin can be written as \( \frac{a}{b} \), where \(a\) and \(b\) are coprime integers. Find \(a+b \).

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