Gotta catch...half of them

Sacha wants to start a collection of Brillimon cards. He knows for a fact that :

• a tenth of the $120$ Brillimon has a $\frac{1}{3}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{5}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{6}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{10}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{15}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{20}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{30}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{40}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{60}$ chance of being in a $10$ -cards bundle.
• a tenth of the $120$ Brillimon has a $\frac{1}{120}$ chance of being in a $10$ -cards bundle.

How many $10$ -cards bundles should he purchase at least in order to expect to complete half of his Brillimon collection ?