Chapter 13 - Counting and Probability - 13.1 Counting - 13.1 Asses Your Understanding - Page 847: 28

$550$

Here $A$ is the set attending to the session I and $B$ is the set attending to the session II. According to the counting formula we know that $n(A\cup B)=n(A)+n(B)-n(A\cap B).$ Hence here $n(A\cup B)=n(A)+n(B)-n(A\cap B)=15+20-10=25.$ Hence: $n(A\cup B)=200+150-75=275.$ We know that $275$ students attend neither of the lectures, hence in total there are $275+275=550$ students participated.