For proton and electron of identical energy encounter same potential

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For proton and electron of identical energy encounter same potential barrier .For which probability of transmission greatest?
 
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That depends on the exact height and length of the barrier as well as the energy of the incident particles. For a given height and length of the barrier you can find an energy less than the height of the barrier for which either particle would have a transmission probability of 1 and the other particle would have something less than 1.

You can see a decent treatment of the problem on Wikipedia. Take a look at the form of the transmission coefficient T for the case E<V_0. If you choose k_1 such that \sin(k_1 a) = 0 then the transmission coefficient will be 1. k_1 depends on the mass of the particle and the difference between the height of the barrier and the energy of the particle.
 

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