We have a "universal set" T of 240 students, and 3 its subsets:


    - subset H of 176 students on honor roll;

    - subset V of 48 students of the varsity team;  and

    - subset HV 36 students that are in the honor roll and also members of the varsity team.


So, the subset HV is simply intersection of the sets H and V.


The probability under the question is the ratio of the number of elements in the UNION of the sets H and V 
to the total number of elements of the "universal set" T.


So we need to determine the number of elements in the UNION  (H U V).


For it, use the formula of the elementary set theory


    n(H U V) = n(H) + n(V) - n(HV).     (*)


In this way, you will get


    n(H U V) = 176 + 48 - 36 = 188.


Now the probability under the question is


    P =  =  =  = 0.7833 = 78.33%.      ANSWER

    To calculate the number of elements in the union of two finite subsets, we first add the numbers of elements in each  
    of the two subsets, and then subtract the number of elements in the intersection set, since we counted these elements twice.