Keep shooting until you win!

Discrete Mathematics Level pending

Suppose Lucy and Peter shoot independently until each shoots each other perfectly.They have probabilities \(\frac{2}{5}\) and \(\frac{3}{7}\) of shooting each other perfectly at each shot respectively.Find the probability that Peter will require more shots than Lucy.

The answer is in the form \(\frac{a}{b}\) where a and b are co-prime.

Find a+b .

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