Question

A group of 72 children completed a survey on what kind of activity they like. The choices were: Chess, Swimming, and Football. Everyone liked at least one activity except 7 kids, who don't like any of these three kinds of activities.
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.

Answer 1

1) Find the number of kids who liked Swimming and Football.
2) What is the probability that a randomly-chosen child from this group likes either Chess or Swimming but not Football?
3) What is the probability that a randomly-chosen child from this group does not like physically active activities?

Answer 2

Draw your Venn diagram. The first 4 numbers are easy to fill in.
Now let x be those who liked all three
Let F be those who liked only football
Let S be those who liked only swimming
40 liked swimming, and 16+8+x of those liked something else. So,
24+x+S = 40
Similarly,
20+x+F = 32
F+x+S = 19
Solve that and you have
F=3, S=7, x=9
Questions:
(1) 55
(2) 62/65
(3) 7/72