Please see page 30 here http://www.cs.utexas.edu/~jason777/School/introduction%20to%20probability%20(bertsekas,%202nd,%202008).pdf and also page 28 which defines the Total Probability Theorem.

I'm confused at the end of page 30 (the equation that starts with P(U3) =

Now, the Total Probability Theorem states a set A is required which is a partition of the sample space. But the set B which is included with U in this equation cannot be a partition since the union of its elements does not equal the sample space.

Where did this equation come from?

Question

Please see page 30 here http://www.cs.utexas.edu/~jason777/School/introduction%20to%20probability%20(bertsekas,%202nd,%202008).pdf and also page 28 which defines the Total Probability Theorem.

I'm confused at the end of page 30 (the equation that starts with P(U3) = 

Now, the Total Probability Theorem states a set A is required which is a partition of the sample space. But the set B which is included with U in this equation cannot be a partition since the union of its elements does not equal the sample space.

Where did this equation come from?