Question

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.


What is the probability that a randomly-chosen child from this group does not like active kinds of sport?

Answer 1

`(17)/(72)`

Explanation:

From the given information:

Total number of students,
`n(U)=72`

The choices were: Chess(C), Swimming(S), and Football(F).

Everyone liked at least one sport except 7 kids,
`n( C \cup F \cup S)'=7`

Chess is not an active sport; and

10 children liked Chess only,
`n( C \cap F' \cap S')=10`

The probability that a randomly-chosen child from this group does not like active kinds of sport is the Probability that a student plays chess only or like no kind of sport at all.

`P( C \cup F \cup S)'+P(C \cap F' \cap S')=(n( C \cup F \cup S)'+n(C \cap F' \cap S'))/(n(U)) \\=(10+7)/(72) \\=(17)/(72)`