Tigers

Level pending

Jo-Ann hunts tigers. She knows that in an area lives 5 tigers. There is a 2/7 probability that she eats the tiger, there is a 3/7 probability that the tiger eats her, and there is a 2/7 probability that they eat each other. The probability that she survives all 5 tigers is a fraction \(\frac{a}{b}\). What is the sum of the digits of \(a\) plus the sum of digits of \(b\)?

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