A group of 72 children completed a survey on what kind of sport they like. The choices were: Chess, Swimming, and Football. Everyone liked at least one sport except 7 kids, which doesn't like any of these three kind of sports. 12 children liked Chess and Football but not Swimming, 16 children liked Chess and Swimming but not Football, 8 children liked Swimming and Football but not Chess, 10 children liked Chess only, 40 children liked Swimming, 32 student liked Football. a)Find the number of kids who liked Swimming and Football.
b)What is the probability that a randomly-chosen child from this group likes either Chess or Swimming but not Football?
c)What is the probability that a randomly-chosen child from this group does not like active kinds of sport?

see below

Step-by-step explanation:

Let C = chess

S = swimming

F = football

x = football only

y = all three sports

z = swimming only

x+y+ 8+12 = 32  those who like football

y+z+8+16 = 40  those who like swimming

7+x+8+y+12+10+16+z = 72  all children

Simplifying these equations

x+y = 32-20 = 12

y+z = 40-24 = 16

x+y +z = 72-53 = 19

Substituting x+y = 12 into the last equation

12 +z = 19

z = 7

y+z = 16  

y = 9

x+y =12

x =5

Swimming  only is 7

Football only is 5

Swimming and football y+8 = 9+8 = 17

P( chess or swimming but not football) = (10+16+z)/ total

                                                                 =(10+16+7)/ total

                                                                 =33/72

P( no  active sport) = chess only or no sport/total

                                 =(10+7)/72