Are you referring to the 08 and 09 cards or just cards with 8 and/or 9 in any position?

There are two cards 08 and 09, so on any draw the probability of drawing one or other of these is 2/100=1/50, and the probability that neither are drawn is 49/50. Since you are drawing with replacement this probability is the same for each draw.

So what is the probability that in 16 draws neither appear? (these are 16 independent draws each with the same probability of not drawing the 08 or 09 cards)

CB