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 a b \frac{a}{b} . What is the sum of the digits of a a plus the sum of digits of b b ?


The answer is 27.

Bob Yang by Bob Yang , 23, USA

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1 solution

Dear Bob,

What did you mean by "eat each other"? *scared face *

Answer:

She will only survive if she eats the tiger. So the probability that she eats all 5 tigers can be written as

2 5 7 5 ⇒ 32 16807 \dfrac{2^5}{7^5} \Rightarrow \dfrac{32}{16807} .

As seen, the sum of digits of ( a ) (a) is 5 5 and the sum of digits of ( b ) (b) is 22 22 . Thus, our desired answer is 27 27 .

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