# Another question

#### warwick

##### Full Member
http://i111.photobucket.com/albums/n149 ... 1298605295

I think I understand the first conclusion. The probability of the union of the disjoint sets is the sum of the probabilities. As k tends to infinity, this pairwise disjoint set tends to the limit of the union which in this case would be the sample space. The limit of the union could be something else, but it's less than or equal to the probability of the sample space.

I'm not exactly sure about the last one.

#### pka

##### Elite Member
The last one comes from properties of convergent series.
If a series converges then the ‘tail’ of the series must converge to zero.