Is my probability of getting Merlin accurate?

5 stars servants share a 1% chance of showing up in a roll.
I've read that when merlin shows up, his banner will give him a .7% chance of getting him per roll which means that other 5 star servants in the roll will share the remaining .3% to make up the 1% chance of showing up.
And if my probability analysis is correct, the chance of Merlin NOT showing up is 99.3%. I plan to spend all my quartz for him and I think I will reach 300+ quartz by the time he shows up.
so that will give me 100 rolls.
So if I roll for him 100 times, the formula of NOT getting him would be:
0.993^100=0.49 which means that the the chance of getting him is 1-0.49=0.51 or 51%. Is my formula right?