Probability of hunting

[Guest]

A lion will reach a river to drink water randomly between 5 PM and 5.40 PM , it will stay for 20 minutes and then leave . A tiger will reach the river at a random time between 5 PM and 5.50 PM , it will stay for 10 minutes and then leave .
A hunter will arrive the river at a random time from 5 PM to 6 PM . If both the beast are there , he will have 2/3 chance to shoot the lion and 1/3 chance to shoot the tiger . Find
(1) The probability that the 2 beast will meet at there from 5 PM to 6 PM .
(2) The probability that the lion will be shot within that hour .

[Guest]

( Additional information )
If only 1 or 0 beast is there , the hunter will leave immediately .