We are given
[tex] P(A)=\frac{1}{6} [/tex]
[tex] P(B)=\frac{3}{5} [/tex]
P(A∩B)=[tex] \frac{1}{10} [/tex]
Two events A and B are independent when
P(A∩B)=[tex] P(A)*P(B) [/tex]
so, we can plug values and check it
[tex] \frac{1}{10} =\frac{1}{6} *\frac{3}{5} [/tex]
now, we can simplify right side
[tex] \frac{1}{10} =\frac{3}{6*5} [/tex]
[tex] \frac{1}{10} =\frac{1}{10} [/tex]
we can see that
both sides are equal
so, events A and B are independent .............Answer
