Chances Are
A full solution was received from Andrei of School 205 Bucharest. Joseph Yu from:HKMA David li Kwok Po College and La Viseis of the Preah Sisovath also sent solutions for the "best bet".
The probability of the "toss coin" is: 1 / (2 to the power 12) = 1 / 4096
The probability of the "Famous snaps" 1 / (10 x 9 x 8 x 7) = 1 / 5040
The probability of the "Throw five dice" 1 / (6 to the power 5) = 1 / 7776
The probaility of the " ten side dice" 1 / (10 to the power 4) = 1 / 10000
The probaility of the "Gardener" 1 / (7 x 6 x 5 x 4 x 3 x 2 x 1) = 1 / 5040
So "Toss coin" has the highest chance to win!