Question 1206319
<pre>
I am quite sure that this student's instructor's standard notation
is for the subscripted S's, S1, ... Sn to form a partition of set A,
where all S's are mutually disjoint and their union is A.

So I don't think it necessary that the student state that the S's are
mutually disjoint nor than their union is the set A.  However, this 
student must know this to use the law of total probability. 

The Law of Total Probability states:

Given a partition of A, that is, n mutually disjoint sets 
S1, S2, ... Sn

such that S1 U S2 U ... U Sn = A, 
then  

P(A) = P(A ∩ S1) + P(A ∩ S2) + ... + P(A ∩ Sn) =

P(A|S1)P(S1) + P(A|S2)P(S2) + ... + P(A|Sn)P(Sn)  

Here n=2

{{{"P(A)"}}}{{{""=""}}}{{{"P(A|S1)"*"P(S1)"+"P(A|S2)"*"P(S2)"}}}

{{{"P(A)"}}}{{{""=""}}}{{{0.2*0.7+0.1*0.3}}}{{{""=""}}}{{{0.17}}}

Edwin</pre>