I would like to know if the Law of Total Probability can work in a case where the sample space is not partioned, at least, not entirely. Like this: 

[![enter image description here](https://i.stack.imgur.com/1o3OD.png)](https://i.stack.imgur.com/1o3OD.png)

In this specific situation, A1, A2 and A3 are disjoint but A4 and A5 are not, in this case, couldn't I calculate the probability of B as:

$$
 \displaystyle \sum\_{i=1}^3 P(B|A\_i)P(A\_i)
$$ 
which is the same as
$$ 
P(B) =P(B|A\_1)P(A\_1)+P(B|A\_2)P(A\_2)+P(B|A\_3)P(A\_3)
$$

When I think about it I don't see why that wouldn't be possible. If someone can explain I would be thankful.