[bigpooch]

You are overcounting the situations where you receive more
than one of the two key cards. Of the C(49,4)=211876
combinations, you get these number of combinations for:

2 key cards: 4 x 4 x C(49-2x4,2) = 16C(41,2) = 13120
3 key cards (pair): 2xC(4,2)x4x41 = 2x6x4x41 = 1968
"two pairs" of key cards: C(4,2)xC(4,2) = 6x6 = 36
"trips" with key cards: 2xC(4,3)x4 = 2x4x4 = 32

total: 15156
probability ~ 0.07153240575