A. The probability that a student who has chores also has a curfew.
The total number of students that have chores is 75.
Out of these 75, 51 also have a curfew.
So, the probability that a student who has chores also has a curfew is;
[tex]\frac{51}{75}[/tex]
B. The probability that a student who has a curfew also has chores.
The total number of students that have a curfew is 81.
Out of these 75, 51 also have chores.
So, the probability that a student who has a curfew also has chores is;
[tex]\frac{51}{81}[/tex]
C. To check for independence between the 2 events (chores and curfew), we perform a p-test of independence.
The square is a 2 x 2 square, therefore, the degree of freedom is (2-1)(2-1)=1
The chi-square value is;
[tex]\chi^2=0.149[/tex]
We obtain the p-value as;
[tex]p=0.6999[/tex]
Since p > 0.05, the events chores and curfew are independent.
