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Answer:
A) check attached picture
B) 272
C) 0.4478
Step-by-step explanation:
From the information given ;
A) The Venn diagram of the information can be found in the attached picture.
B) Number of students involved in both team sports and music.
n(student in sports team) = 385
n(students involved in music) = 450
Number of students involved in both music and team sport = y
Number of students not involved in either team sport or music = 87
Total number of students = 650
Therefore,
n(music alone) = 450 - y
n(team sport alone) = 385 - y
Adding the following:
n(music alone) + n(team sport alone) + n( both music and team sport) + n(neither music nor team sport) = Total number of students
450 - y + 385 - y + y + 87 = 650
922 - y = 650
922 - 650 = y
y = 272
Therefore, number of students involved in both music and team sport = 272
C) probability of being involved in team sport or in music.
P(being involved in music) = (450 - 272) / 650 = 0.2738
P(being involved in team sport) = (385 - 272) / 650 = 0.1738
P(involved in both) = 272 / 650 = 0.4184
P(involved in neither) = 87 / 650 = 0.1338
P(being involved in team sport) or p(being involved in music)
P(being involved in team sport) + p(being involved in music)
0.1738 + 0.2738 = 0.4478
