Luke The Cat 2Discrete Mathematics Level pending
Based on the original Luke the cat problem by Yuxuan Seah
Luke the cat spies a mouse 10m away. Luke travels at 4 metres per second while the mouse is running away at 2 metres per second. When Luke reaches the mouse, he will start swiping at it once every second, while maintaining a speed equal to the mouse. However, Luke is tired and hungry and can only kill 1/3 of the time. He will just cripple the mouse 1/3 of the time and miss completely 1/3 of the time. If he cripples the mouse, his next swipe will kill without fail. The mouse hole is 24m away from Luke. The probability that Luke kills the mouse is a/b, where a and b are coprime integers. Find ab.
Note: Luke can attack the instant he catches up with the mouse, and can attack again on the second that the mouse dives into his hole.