You need to give more information about the contents of the set of 7. Are they (i) seven randomly chosen cards, or (ii) seven different cards, but otherwise random?

In case (i) or (ii) the first card is a randomly chosen card out of 100 and the chance that it is one of the two you want is 2/100 = 1/50.

In case (i) the chance that each of the seven cards is not one you want is 98/100 and so the chance that all seven are not ones you want is (98/100)^7. In case (ii) the chance that the seven are drawn from the 98 you don't want as opposed to being drawn from all 100 possible is 98-choose-7 / 100-choose-7 = (98!/91!.7!)/(100!/93!.7!) = 98!.93!.7! / 100!.91!.7! which fortunately cancels down to 93.92/100.99.