In a survey of 250 members of a local sports club 150 member

In a survey of 250 members of a local sports club, 150 members indicated that they plan to attend the next Summer or Winter Olympic Games, 125 members indicated that they plan to attend the next Summer Olympic Games, and 75 indicated that they plan to attend the next Winter Olympic Games. How many members of the club plan to attend Both of the games? 250 members Exactly one of the games? boo 200 members The Summer Olympic Games only? 125 members None of the games? 0 members Let A, B, and C be sets in a universal set U. We are given n(U) = 54, n(A) = 27, n(B) = 29, n(C) = 26, n(A interset B) = 11, n(A interset C) = 10, n(B interset C) = 17, n(4 interset 8 interset C^c) = 5. Find the following values. n((A union B union C)^C) n(A^c interset B^C interset C)

Solution

4) Let x members attend both summer and winter olympics

So, only summer olympics = 125-x

only winter olympics = 75 -x

Total = 250

Either of games = 150

So, x+ 125-x +75-x = 150

200 -x = 150

x = 50

So, a) 50 members attend both

b) Exactly on of games:

only summer olympics = 125 -50 = 75

only winter olympics = 75-50 = 25

Exactly on of games: = 100

c) Summer olympic game only = 75

d) None of the games = 250 -150 = 100

x =