In a school of 685 students, there are 385 students involved in sports teams, and there are 450 involved with the music program. There are 87 students that are not involved in either program.
There are some students involved in both programs.
a) Draw a Venn diagram to represent this situation.
b) Use the additive principle of non-mutually exclusive sets to determine the number of students that
are involved in both team sports and music.
c) Use the additive principle for the probability of non-mutually exclusive events to determine the
probability of a student being involved in team sports OR involved in music.

 a) see image (below)

                b) S ∩ M = 237

                c) S U M = 598

Step-by-step explanation:

b) Total students = 685

   Not sports or music = 87

   Sports Total = 385

   Music Total = 450

Both Sports and Music is their intersection:

S ∩ M = S + M + N -  T

          = 385 + 450 + 87 - 685

          = 237

c) Sports only = S - (S ∩ M)

                       = 385 - 237

                       = 148

Music only = M - (S ∩ M)

                  = 450 - 237

                  = 213

Sports OR Music is their union:

S U M = S + M - (S ∩ M)

          = 385 + 450 - 237

          = 598

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step-by-step explanation: