Answer to Question #145900 in Statistics and Probability for rwan alqmash

Question

A class consists of 100 students, 60 students like music, 70 students like football,
and 30 students like football and music. A student is chosen randomly, what is
the probability that:
a. He likes music only.
b. He doesn't like music or football.
c. He doesn't like music and football.

Answer 1

if 60 students like music and 30 like music and football, means 30 students like only music.

if 70 students like football and 30 like music and football, means 40 students like only football.

a) When we randomly choose 1 student we have 100 variants, from them in 30 variants we choose a student that likes music only. The corresponding probably is

$\frac {30} {100} = 0.3$

b) When we randomly choose 1 student we have 100 variants, from them in $100-30-40-30=0$ (30 is number of students that like football and music, 40 is number of students that like music , 30 is number of students that like music, 40 is number of students that like football , 30 is number of students that like football and music) variants we choose a student that likes music only. The corresponding probably is

$\frac {0} {100}=0$

c) When we randomly choose 1 student we have 100 variants, from them in $100-30=70$ (30 is number of students that like football and music) variants we choose student that likes music only. The corresponding probability is

$\frac {70} {100}=0.7$